Find the exact value of each of the remaining trigonometric functions of theta

In summary, finding the exact value of trigonometric functions is important for accurately calculating ratios between the sides of a right triangle, which is useful in various real-world applications. The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. You can find the exact value of a trigonometric function by using a calculator, reference table, or manually calculating using the definitions of the functions and the given angle. The symbol "theta" (θ) represents an angle in a right triangle in trigonometry. Common techniques for finding the exact value of trigonometric functions include using special triangles, the Pythagorean theorem, trigonometric identities, and the unit circle.
  • #1
adrianaiha
1
0
sin\theta 3/5
 
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  • #2
I've moved this thread to our Trigonometry forum, since this is not a calculus problem, but involves trig. instead.

I am assuming you've been given:

\(\displaystyle \sin(\theta)=\frac{3}{5}\)

And you are to find the values of the other 5 trig. functions as a function of $\theta$.

Since the sine of $\theta$ is positive, we know that $\theta$ is in either Quadrant I or II. To find the cosine of $\theta$, let's consider the Pythagorean identity:

\(\displaystyle \sin^2(\theta)+\cos^2(\theta)=1\)

Solve this for $\cos(\theta)$, and plug in the given value for $\sin(\theta)$...what do you get?
 

FAQ: Find the exact value of each of the remaining trigonometric functions of theta

1. What is the purpose of finding the exact value of trigonometric functions?

The exact value of trigonometric functions allows us to accurately calculate the ratios between the sides of a right triangle, which is essential for solving various real-world problems in fields such as engineering, physics, and navigation.

2. What are the six basic trigonometric functions?

The six basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

3. How do I find the exact value of a trigonometric function?

To find the exact value of a trigonometric function, you can use a calculator or reference table, or you can use the definitions of the functions and the given angle to manually calculate the value.

4. What does the "theta" symbol represent in trigonometry?

In trigonometry, "theta" (θ) is commonly used to represent an angle in a right triangle. It is usually the angle opposite the side being referenced in a trigonometric function.

5. What are the common techniques for finding the exact value of trigonometric functions?

Some common techniques for finding the exact value of trigonometric functions include using special triangles, the Pythagorean theorem, and trigonometric identities. Additionally, using the unit circle and the values of sine and cosine for common angles can also be helpful.

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