Question

Please help me right now.

Answer 1

Look at the picture.

Definitions:

`\sin\theta=(y)/(r)\\\\\cos\theta=(x)/(r)\\\\\tan\theta=(y)/(x)\\\\\cot\theta=(x)/(y)\\\\\sec\theta=(1)/(\cos\theta)=(r)/(x)\\\\\csc\theta=(1)/(\sin\theta)=(r)/(y)`

We have:

`\sec\theta=3=(3)/(1)` and Quadrant I (x > 0, y > 0)

Therefore r = 3 and x = 1. Calculate y:

`r=√(x^2+y^2)\to√(1^2+y^2)=3\ \ \ |^2\\\\1+y^2=9\ \ \ |-1\\\\y^2=8\to y=\sqrt8\\\\y=√(4\cdot2)\to y=\sqrt4\cdot\sqrt2\to y=2\sqrt2`

Substitute to the formula of tan:

`\tan\theta=(2\sqrt2)/(1)=2\sqrt2`

Answer: a.