Question

1. based on the figure, select all true equations.

a (cos(45^circ) = a)
b (cos(45^circ) = b)
c (sin(45^circ) = b)
d (sin(45^circ) = a)
e (\tan(45^circ) = a)
f (\tan(45^circ) = b)
right triangle with right angle at c, angle at a is (45^circ), sides: ac = b, bc = a, ab = c

Explanation:

Step1: Recall cosine definition

For $\angle A = 48^\circ$, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{c}$

Step2: Recall sine definition

For $\angle A = 48^\circ$, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{a}{c}$

Step3: Recall tangent definition

For $\angle A = 48^\circ$, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b}$

Step4: Match to given options

Compare each option to the trigonometric ratios derived.

Answer:

b. $\cos(48^\circ) = \frac{b}{c}$
c. $\sin(48^\circ) = \frac{a}{c}$
e. $\tan(48^\circ) = \frac{a}{b}$