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?

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

Q: Which of the following is the correct set of six trigonometric ratios for $$\theta in $$the triangle shown?

$$\sin \theta = \frac{\sqrt{5}}{3},\ \cos \theta = \frac{2}{3},\ \tan \theta = \frac{\sqrt{5}}{2},\ \csc \theta = \frac{3}{\sqrt{5}},\ \sec \theta = \frac{3}{2},\ \cot \theta = \frac{2}{\sqrt{5}}$$

Q: If the triangle is reflected over the y-axis, which trigonometric ratios for $$\theta$$ would change sign?

$$\cos \theta$$ and $$\sec \theta$$

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

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

Question 7

If the triangle is scaled so that the hypotenuse is 6, what is the new length of the side adjacent to $$	heta$$?

Accepted Answer

4

Question 8

If $$	heta is an $$angle in a right triangle where the adjacent side is 2 and the hypotenuse is 3, what is the length of the side opposite $$	heta$$?

Accepted Answer

$$\sqrt{5}$$

Question 9

Which of the following is the correct set of six trigonometric ratios for $$	heta in $$the triangle shown?

Accepted Answer

$$\sin 	heta = \frac{\sqrt{5}}{3},\ \cos 	heta = \frac{2}{3},\ 	an 	heta = \frac{\sqrt{5}}{2},\ \csc 	heta = \frac{3}{\sqrt{5}},\ \sec 	heta = \frac{3}{2},\ \cot 	heta = \frac{2}{\sqrt{5}}$$

Question 10

If the triangle is reflected over the y-axis, which trigonometric ratios for $$	heta$$ would change sign?

Accepted Answer

$$\cos 	heta$$ and $$\sec 	heta$$

Finding the Six Trigonometric Ratios for a Right Triangle

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