Question

question 9 (mandatory) (1 point)
which equation is the quotient identity?
( \bigcirc ) a) ( \tan \theta=\frac{sin \theta}{cos \theta} )
( \bigcirc ) b) ( \tan \theta=\frac{1}{cos \theta} )
( \bigcirc ) c) ( \tan \theta=\frac{1}{sin \theta} )
( \bigcirc ) d) ( \tan \theta=\frac{cos \theta}{sin \theta} )
question 10 (mandatory) (1 point)

Explanation:

The quotient identity in trigonometry for tangent is defined as the ratio of sine to cosine. Let's analyze each option:

• Option a: $\tan\theta=\frac{\sin\theta}{\cos\theta}$ is the standard quotient identity for tangent.
• Option b: $\frac{1}{\cos\theta}=\sec\theta$ (reciprocal identity for secant, not tangent).
• Option c: $\frac{1}{\sin\theta}=\csc\theta$ (reciprocal identity for cosecant, not tangent).
• Option d: $\frac{\cos\theta}{\sin\theta}=\cot\theta$ (quotient identity for cotangent).

Answer:

A. $\tan\theta=\frac{\sin\theta}{\cos\theta}$