Question

The point (2, 3) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

Answer 1

So can you explain that? lol

Answer 2

it is the representation of your problem

Answer 3

now, we can write this:
\[\Large OP = \sqrt {{2^2} + {3^2}} = ...\]

Answer 4

what is OP?

Answer 5

I have applied the Theorem of Pitagora to the triangle OP1P

Answer 6

the sin tan and cos?

Answer 7

yes, we have to compute OP first

Answer 8

ok

Answer 9

hint:
\[\Large OP = \sqrt {{2^2} + {3^2}} = \sqrt {4 + 9} = ...?\]

Answer 10

is it just square root of 13

Answer 11

yes!

Answer 12

so thats the answer

Answer 13

for all three

Answer 14

no, since we have to apply these formulas:
\[\Large \begin{gathered}
\cos \theta = \frac{{O{P_1}}}{{OP}} = \frac{2}{{\sqrt {13} }} = ... \hfill \\
\hfill \\
\sin \theta = \frac{{P{P_1}}}{{OP}} = \frac{3}{{\sqrt {13} }} = ... \hfill \\
\end{gathered} \]

Answer 15

finally, by definition, we can write:
\[\Large \tan \theta = \frac{{P{P_1}}}{{O{P_1}}} = ...\]

Answer 16

3/2?

Answer 17

yes!

Answer 18

sweet thanks for the help!

Answer 19

:)