Question

question 9
in which quadrant is the secant trig ratio positive and the tangent trig ratio negative?
quadrant 3
quadrant 4
quadrant 2
quadrant 1
question 10
150° and -210° are coterminal angles.
true
false

Explanation:

Step1: Recall trig - ratio signs in quadrants

Secant is the reciprocal of cosine ($\sec\theta=\frac{1}{\cos\theta}$). Cosine is positive in Quadrants 1 and 4. Tangent ($\tan\theta=\frac{\sin\theta}{\cos\theta}$) is negative when sine and cosine have opposite signs. In Quadrant 4, cosine is positive and sine is negative, so tangent is negative.

Step2: Determine the quadrant

Since secant (same sign as cosine) is positive and tangent is negative, the quadrant is Quadrant 4.

Step3: Recall the concept of coterminal angles

Coterminal angles differ by a multiple of 360°. To check if 150° and - 210° are coterminal, find the difference: $150-(-210)=150 + 210=360$. Since the difference is 360°, they are coterminal angles.

Answer:

Question 9: B. Quadrant 4
Question 10: A. True