Q: Given the right triangle shown, with sides of length 2 (adjacent to $$\theta$$), 3 (hypotenuse), and the unknown opposite side, what is the value of $$\sin \theta$$?

$$\sin \theta = \frac{\sqrt{5}}{3}$$

Q: What is the value of $$\tan \theta$$ for the triangle shown?

$$\tan \theta = \frac{\sqrt{5}}{2}$$

Q: What is the value of $$\csc \theta$$ for the triangle shown?

$$\csc \theta = \frac{3}{\sqrt{5}}$$

Q: What is the value of $$\cot \theta$$ for the triangle shown?

$$\cot \theta = \frac{2}{\sqrt{5}}$$

Question 1

Given the right triangle shown, with sides of length 2 (adjacent to $$	heta$$), 3 (hypotenuse), and the unknown opposite side, what is the value of $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \frac{\sqrt{5}}{3}$$

Question 2

For the same triangle, what is the value of $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \frac{2}{3}$$

Question 3

What is the value of $$	an 	heta$$ for the triangle shown?

Accepted Answer

$$	an 	heta = \frac{\sqrt{5}}{2}$$

Question 4

What is the value of $$\csc 	heta$$ for the triangle shown?

Accepted Answer

$$\csc 	heta = \frac{3}{\sqrt{5}}$$

Question 5

What is the value of $$\sec 	heta$$ for the triangle shown?

Accepted Answer

$$\sec 	heta = \frac{3}{2}$$

Question 6

What is the value of $$\cot 	heta$$ for the triangle shown?

Accepted Answer

$$\cot 	heta = \frac{2}{\sqrt{5}}$$

Finding the Six Trigonometric Ratios for a Right Triangle

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