Question

Given cos(theta)=4/9 and csc(theta)<0, find sin(theta) and tan(theta).

Answer 1

can you help me and i will help you too

Answer 2

@heatherchaloupek2004 What do you need help with hon?

Answer 3

cos(theta)=4/9, then \[\cos ^{2}(\theta)=16/81\]
\[\sin(\theta)=\sqrt{1-\cos^{2}(\theta)}\]
\[\sin(\theta)=\sqrt{1-16/81}=\sqrt{65}/9\]
\[\tan(\theta)=\sin(\theta)/\cos(\theta)=\sqrt{65}/4\]

Answer 4

@SwapnilP so, how do you get to sqrt(65)/9?

Answer 5

Here it is:
\[We have \cos(\theta)=4/9 and \sin(\theta)=\sqrt{65}/9\]
so \[\tan(\theta)=\sin(\theta)/\cos(\theta)=\[(\sqrt{65}/9)/(4/9)=(\sqrt{65}/9)*(9/4)=\sqrt{65}/4\]

Answer 6

\[\sqrt{1-16/81}=\sqrt{(81-16)/81}=\sqrt{65/81}=\sqrt{65}/\sqrt{81}=\sqrt{65}/9\]

Answer 7

LOh I gent it'!