if cos Ⓗ= -4/7 , what are the values of sin Ⓗ and tan Ⓗ ?

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Question

if cos Ⓗ= -4/7 , what are the values of sin Ⓗ and tan Ⓗ ?

help step by step!

turingtest · Answer

what does cosine represent (in terms of opposite, adjacent, hypotenuse)

anonymous · Answer

i know that the formula is  cos(0)=adjacent/hypotenus

anonymous · Answer

@TuringTest

turingtest · Answer

correct, so that means we can draw a picture|dw:1428868205437:dw|now you can fill in the values for the sides

anonymous · Answer

what do you mean by fill the values?

turingtest · Answer

well if cos Ⓗ= -4/7=adjacent/hypotenuse, how long is the adjacent?

anonymous · Answer

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhh do i divie the adjacent and the hypotenuse?

anonymous · Answer

divide*

anonymous · Answer

@TuringTest

turingtest · Answer

no you need to label the picture

turingtest · Answer

$$\cos\theta=-\frac47=\frac{adjacent}{hypotenuse}$$

turingtest · Answer

how long is the adjacent?

anonymous · Answer

oh i get it i subtract the adjacent from the hypotenuse

turingtest · Answer

you have to use the pythagorean theorem

anonymous · Answer

isnt the hypotenuse= to the adjacent and opposite added up together?

anonymous · Answer

oh so a^2+b^2=c^2 ?

turingtest · Answer

yep

anonymous · Answer

give me a second

anonymous · Answer

a^2 + b^2 = c^2
-4^2 + 7^2 = c^2
16 + 49 = c^2
16 + 49 = 65

anonymous · Answer

but for the 65 since its still like to the second power, do i square root it? or divide it by 2 ?

anonymous · Answer

@TuringTest

turingtest · Answer

not quite, a is the opposite side, b is the adjacent side, and c is the hypotenuse

anonymous · Answer

im confused , can you illustrate this for me ?

turingtest · Answer

well again, look at the formula$$\cos \theta= -\frac47=\frac{adjacent}{hypotenuse}$$how long is the adjacent?

anonymous · Answer

-4?

turingtest · Answer

you can ignore the minus sign, so just 4, yeah
so put this on the picture|dw:1428869526075:dw|how long is the hypotenuse?

anonymous · Answer

7?

anonymous · Answer

but what about the negative  sign ?

anonymous · Answer

@TuringTest

turingtest · Answer

that tells you what quadrant you are in. |dw:1428869832426:dw|because the adjacent is negative we know we must be in either quadrant II or III. however this doesn't really matter for us, we just need the lengths of the triangle sides and can figure out the quadrant stuff later.

anonymous · Answer

so the adjacent is 4 and the hypotenuse is 7?

turingtest · Answer

yes|dw:1428870265584:dw|so now go back to the pythagorean theorem:
$$a^2+b^2=c^2\a=\sf adjacent\b=\sf opposite\c=\sf hypotenuse$$