Question

in the triangle above, the cosine of ( a^{circ} ) is 0.8. what is the sine of ( b^{circ} )?

Explanation:

Step1: Use the property of complementary angles in a right - triangle

In a right - triangle, \(a + b=90^{\circ}\), so \(b = 90^{\circ}-a\).

Step2: Apply the trigonometric identity \(\sin(90^{\circ}-\theta)=\cos\theta\)

Since \(b = 90^{\circ}-a\), then \(\sin b=\sin(90^{\circ}-a)\).
According to the co - function identity \(\sin(90^{\circ}-\theta)=\cos\theta\), when \(\theta = a\), we have \(\sin(90^{\circ}-a)=\cos a\).

Answer:

\(0.8\)