Thales of Miletus circa â€” BC is known as the founder of geometry. The legend is that he calculated the height of the Great Pyramid of Giza in Egypt using the theory of similar triangleswhich he developed by measuring the shadow of his staff.

Based on proportions, this theory has applications in a number of areas, including fractal geometry, engineering, and architecture. Often, the angle of elevation and the angle of depression are found using similar triangles. In earlier sections of this chapter, we looked at trigonometric identities.

Identities are true for all values in the domain of the variable. In this section, we begin our study of trigonometric equations to study real-world scenarios such as the finding the dimensions of the pyramids. Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all.

Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period.

In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid.

There are similar rules for indicating all possible solutions for the other trigonometric functions. Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process. However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections.

But the problem is asking for all possible values that solve the equation. Therefore, the answer is. When we are given equations that involve only one of the six trigonometric functions, their solutions involve using algebraic techniques and the unit circle see [link].

We need to make several considerations when the equation involves trigonometric functions other than sine and cosine. Problems involving the reciprocals of the primary trigonometric functions need to be viewed from an algebraic perspective. In other words, we will write the reciprocal function, and solve for the angles using the function.

Also, an equation involving the tangent function is slightly different from one containing a sine or cosine function. As this problem is not easily factored, we will solve using the square root property.

Then we will find the angles. We can solve this equation using only algebra. Not all functions can be solved exactly using only the unit circle.

When we must solve an equation involving an angle other than one of the special angles, we will need to use a calculator. Make sure it is set to the proper mode, either degrees or radians, depending on the criteria of the given problem. Make sure mode is set to radians.Thales of Miletus circa â€” BC is known as the founder of geometry.

The legend is that he calculated the height of the Great Pyramid of Giza in Egypt using the theory of similar triangleswhich he developed by measuring the shadow of his staff. Based on proportions, this theory has applications in a number of areas, including fractal geometry, engineering, and architecture. Often, the angle of elevation and the angle of depression are found using similar triangles. In earlier sections of this chapter, we looked at trigonometric identities.

Identities are true for all values in the domain of the variable. In this section, we begin our study of trigonometric equations to study real-world scenarios such as the finding the dimensions of the pyramids. Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all.

Often we will solve a trigonometric equation over a specified interval. However, just as often, we will be asked to find all possible solutions, and as trigonometric functions are periodic, solutions are repeated within each period. In other words, trigonometric equations may have an infinite number of solutions. Additionally, like rational equations, the domain of the function must be considered before we assume that any solution is valid.

There are similar rules for indicating all possible solutions for the other trigonometric functions.

Solving trigonometric equations requires the same techniques as solving algebraic equations. We read the equation from left to right, horizontally, like a sentence. We look for known patterns, factor, find common denominators, and substitute certain expressions with a variable to make solving a more straightforward process.

However, with trigonometric equations, we also have the advantage of using the identities we developed in the previous sections. But the problem is asking for all possible values that solve the equation. Therefore, the answer is. When we are given equations that involve only one of the six trigonometric functions, their solutions involve using algebraic techniques and the unit circle see [link].

We need to make several considerations when the equation involves trigonometric functions other than sine and cosine.

Problems involving the reciprocals of the primary trigonometric functions need to be viewed from an algebraic perspective.

In other words, we will write the reciprocal function, and solve for the angles using the function. Also, an equation involving the tangent function is slightly different from one containing a sine or cosine function. As this problem is not easily factored, we will solve using the square root property. We can solve this equation using only algebra. Not all functions can be solved exactly using only the unit circle. When we must solve an equation involving an angle other than one of the special angles, we will need to use a calculator.

Make sure it is set to the proper mode, either degrees or radians, depending on the criteria of the given problem. Make sure mode is set to radians. The calculator is ready for the input within the parentheses.

### Ferris Wheel Trig Question

Note that a calculator will only return an angle in quadrants I or IV for the sine function, since that is the range of the inverse sine. Cosine is also negative in quadrant III.This website uses cookies to ensure you get the best experience.

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Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Trigonometry Calculator Calculate trignometric equations, prove identities and evaluate functions step-by-step.

Correct Answer :. Let's Try Again :. Try to further simplify. To prove a trigonometric identity you have to show that one side of the equation can be transformed into the other In a previous post, we learned about trig evaluation. It is important that topic is mastered before continuing Sign In Sign in with Office Sign in with Facebook. Join million happy users! Sign Up free of charge:. Join with Office Join with Facebook. Create my account.

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**Ferris Wheel Trigonometry Problem**

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## Ferris wheel trig problems - Applications of Trigonometry Functions

Play next lesson. That's the last lesson Go to next topic. Still don't get it? Play next lesson Practice this topic. Start now and get better math marks! Lesson: 1. Intro Learn Practice.

Do better in math today Get Started Now. Ferris wheel trig problems 2. Tides and water depth trig problems 3. Spring simple harmonic motion trig problems Back to Course Index.

Don't just watch, practice makes perfect. A Ferris wheel has a radius of 18 meters and a center C which is 20m above the ground.

It rotates once every 32 seconds in the direction shown in the diagram. A platform allows a passenger to get on the Ferris wheel at a point P which is 20m above the ground. Graph how the height h of a passenger varies with respect to the elapsed time t during one rotation of the Ferris wheel.

Clearly show at least 5 points on the graph. Determine a sinusoidal function that gives the passenger's height, h, in meters, above the ground as a function of time t seconds. How high above the ground would a passenger be 18 seconds after the Ferris wheel starts moving? How many seconds on each rotation is a passenger more than 30m in the air?This website uses cookies to ensure you get the best experience.

By using this website, you agree to our Cookie Policy. Learn more Accept. Proving Identities. Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Trigonometric Identities Solver Verify trigonometric identities step-by-step. Correct Answer :.

Let's Try Again :. Try to further simplify. To prove a trigonometric identity you have to show that one side of the equation can be transformed into the other Sign In Sign in with Office Sign in with Facebook.

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### Trigonometry Calculator

Learn more Accept. Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Trigonometric Simplification Calculator Simplify trigonometric expressions to their simplest form step-by-step. Correct Answer :. Let's Try Again :. Try to further simplify. Trig simplification can be a little tricky.

You are given a statement and must simplify it to its simplest form Sign In Sign in with Office Sign in with Facebook. Join million happy users! Sign Up free of charge:. Join with Office Join with Facebook. Create my account.

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