Question

Use the given information to evaluate each expression.

cos(φ) = 4/5,(0° < φ < 90°)

Answer 1

do you have any idea how to start?

Answer 2

no...

Answer 3

what are we supposed to be looking for here?

Answer 4

are we looking for the angle, the other trig functions, what??

Answer 5

sorry

sin(2φ)

Answer 6

cos(2φ)

tan(2φ)

Answer 7

i got it give me a sec

Answer 8

so i got:
\[\sin2\phi=24/25\]
\[\cos2\phi=7/25\]
\[\tan2\phi=24/7\]

Answer 9

and they are all positive since the values lie in the first quadrent

Answer 10

can you should me how you got the answer?

Answer 11

okay first we have to extablis something, we are looking for \[0\le2\phi \le90\].
Solving this inequality we get:\[0\le \phi \le45\]

Answer 12

This means that we are working in the first quadrent, which denotes that all trig functions are positive okay

Answer 13

Now, we want sin2x, cos2x, and tan2x. These allow us to use the double angle fromulas. sin2x=2sinxcosx
cos2x=cos^2x-sin^2x
and
Tan2x=(2tanx)/(1-tan^2x)

Answer 14

now we also know that we are given taht cosx=4/5, which should automatically denote a 3-4-5 triangle. This will then make sinx=3/5 and tanx=3/4

Answer 15

Now all we havet to do is crunch out the equations plugging in the corresponding values into each double angle formula

Answer 16

sin2x=2(3/5)(4/5)=24/5

Answer 17

cos2x=(4/5)^2-(3/5)^2=16/25-9/25=7/25

Answer 18

tan2x=2(3/4)/2-(3/4)^2=(3/2)/(1-9/16)=(3/2)*(16/7)=24/7

Answer 19

and thats that

Answer 20

satisfied??

Answer 21

yes. Thank you.