Answer: cotθ
Step-by-step explanation:
tanθ * cos²θ * csc²θ
= [tex]\dfrac{sin\theta}{cos\theta} * \dfrac{cos\theta*cos\theta}{} *\dfrac{1}{sin\theta*sin\theta}[/tex]
= [tex]\dfrac{cos\theta}{sin\theta}[/tex]
= 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. [tex]\dfrac{\pi}{6}[/tex]
- d. C
- e.[tex]-\dfrac{\sqrt{3}}{3}[/tex]
Explanation:
[tex]\dfrac{17\pi}{6} - \dfrac{12\pi}{6} = \dfrac{5\pi}{6}[/tex]
a) Quadrant 2 is: [tex]\dfrac{\pi}{2} < \theta < \pi[/tex]
b) In Quadrant 2, cos is negative and sin is positive, so tan is negative
c) [tex]\pi-\dfrac{5\pi}{6}[/tex] = [tex]\dfrac{\pi}{6}[/tex]
d) the reference line is above the x-axis so it is negative --> [tex]-tan\dfrac{\pi}{6}[/tex]
e) [tex]tan(\dfrac{5\pi}{6})=\dfrac{1}{-\sqrt{3}}=-\dfrac{\sqrt{3}}{3}[/tex]
