Question

practice/homework: find the exact values of the three trigonometric functions of \\(\theta\\).

1. a right triangle with legs 3 and 4, hypotenuse 5, and angle \\(\theta\\) adjacent to side 3.
2. a right triangle with legs \\(7\sqrt{3}\\) and 7, hypotenuse 14, and angle \\(\theta\\) adjacent to side \\(7\sqrt{3}\\).
3. a right triangle with hypotenuse 34, leg 30, and angle \\(\theta\\) adjacent to the unknown leg.
4. in the triangle below, compare and contrast the trig ratios for angle x and angle z. can you make any connections between them?

Explanation:

Identify sides and ratios for Triangle 1

$$
LATEXBLOCK0
$$

Identify sides and ratios for Triangle 2

$$
LATEXBLOCK1
$$

Identify missing side and ratios for Triangle 3

$$
LATEXBLOCK2
$$

Answer:

Question 1

$$ \sin\theta = \frac{4}{5},\quad \cos\theta = \frac{3}{5},\quad \tan\theta = \frac{4}{3} $$

Question 2

$$ \sin\theta = \frac{1}{2},\quad \cos\theta = \frac{\sqrt{3}}{2},\quad \tan\theta = \frac{\sqrt{3}}{3} $$

Question 3

$$ \sin\theta = \frac{15}{17},\quad \cos\theta = \frac{8}{17},\quad \tan\theta = \frac{15}{8} $$