Inverse Trigonometric Functions
Multiple Correct
Premium Question
Grade 12
Question:
Let $\alpha = 3 \sin^{-1} \frac{6}{11}$ and $\beta = 3 \cos^{-1} \frac{4}{9}$. Which of the following are correct? (one or more)
(1) $\cos \beta > 0$
(2) $\cos(\alpha + \beta) > 0$
(3) $\sin \beta < 0$
(4) $\cos \alpha < 0$
Step-by-Step Solution
Key Concept: Show $\alpha > \pi/2$ using $\sin^{-1}(6/11) > \pi/6$ and $\beta > \pi$ using $\cos^{-1}(4/9) > \pi/3$. Then determine the quadrant of each and of $\alpha + \beta$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2), (3), (4)