Question

Help me with these math questions....

Answer 1

Answer: cotθ

Step-by-step explanation:

 tanθ * cos²θ * csc²θ

=  $\dfrac{sin\theta}{cos\theta} * \dfrac{cos\theta*cos\theta}{} *\dfrac{1}{sin\theta*sin\theta}$

= $\dfrac{cos\theta}{sin\theta}$

= cotθ

Answer: B

Step-by-step explanation:

The parent graph is y = x²

The new graph y = -x² + 3 should have the following:

• reflection over the x-axis
• vertical shift up 3 units

Answers:

• a. Quadrant II
• b. negative
• c. $\dfrac{\pi}{6}$
• d. C
• e.$-\dfrac{\sqrt{3}}{3}$

Explanation:

$\dfrac{17\pi}{6} - \dfrac{12\pi}{6} = \dfrac{5\pi}{6}$

a) Quadrant 2 is: $\dfrac{\pi}{2} < \theta < \pi$

b) In Quadrant 2, cos is negative and sin is positive, so tan is negative

c) $\pi-\dfrac{5\pi}{6}$ = $\dfrac{\pi}{6}$

d) the reference line is above the x-axis so it is negative -->  $-tan\dfrac{\pi}{6}$

e) $tan(\dfrac{5\pi}{6})=\dfrac{1}{-\sqrt{3}}=-\dfrac{\sqrt{3}}{3}$