Question

how do I find the exact value of the expression cos60 + tan60

Answer 1

cos = adj over hyp
tan = opp over adj

Answer 2

WELL, I don't want to do the tan(a+b) rule, and I don't remember it, so

cos60 + tan60 =
=cos60 + sin60/cos(60)
=cos^2 60/cos(60) + sin60/cos(60)
={ cos^2 60 + cos(60) }/cos(60)
(draw a 30-60-90 triangle, you will know that:)
sin(60)=sqrt3 /2
cos(60)=1 /2
(therefore) cos^2(60)=1/4

={ 1/4 + 1/2 }/ (sqrt3/2)
={ 1/4 + 2/4 }/ (sqrt3/2)
={ 3/4 }/ (sqrt3/2)
={ 3/2 }/ (sqrt3)

= 3 / { 2 sqrt3 }

Answer 3

don't know why I did all that, but I like playing.

Answer 4

omg @WHAT?! you just confused the heck out of me xD

Answer 5

my 3rd line is supposed to be cos^2(60)+sin(60) on top of the fracion.

Answer 6

I did everything after that right though.

Answer 7

no I did not.

Answer 8

One method looks like it's done geometrically, another arithmetically

Answer 9

just ignore me... and I know my mistake so no need rebuking me over it so much. you certainly can.

Answer 10

Here's the fixed version of WHAT?!'s method:

\[\cos(60)+\tan(60)=\cos(60)+\frac{\sin(60)}{\cos(60)} = \frac{\cos^2(60)+\sin(60)}{\cos(60)}=\frac{0.25+ \frac{\sqrt{3}}{2}}{0.5}\]
\[0.5+\sqrt{3}\]

Answer 11

tom why does cos60 plus tan 60 equal cos60 plus sin60/cos60

Answer 12

Think about it: \[60^\circ = \frac{\pi}{3}\]\[\cos\left(\frac{\pi}{3}\right)= ~?\]\[\tan\left(\frac{\pi}{3}\right)=~?\]

Answer 13

where is the sine coming from?

Answer 14

I am not supposed to use a calculator

Answer 15

no calculator needed.

Answer 16

tan = sin over cos

Answer 17

\[\cos(60)+\tan(60)=\frac{\cos^2(60)}{\cos(60)}+\frac{\sin(60)}{\cos(60)}=\frac{\cos^2(60)+\sin(60)}{\cos(60)}\]

Answer 18

what I am so confused

Answer 19

You want a common denominator @Benghazi, so we change cos(60) into cos^2(60)/cos(60) then we can combine the two fractions.

Answer 20

I understand the need for a common denominator but wouldn't you have to do something like cancellation or distribution or something like that. What you do on one side you do to the other.

Answer 21

tan equal sine over cosine is that correct?

Answer 22

if that confused you just find cos(60) and tan(60)
then add those results

Answer 23

^

Answer 24

i like jiggly's drawing

Answer 25

and you should love it too
because it can help you find cos(60) and tan(60)

Answer 26

freckles explain to me How I would use it. Like I literally do not know how

Answer 27

cos(60)=adj side to the angle with measure 60/hyp

Answer 28

\[\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\]\[\tan\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \cdot \frac{2}{1} = \sqrt{3}\]\[\cos(60)+\tan(60) = \cos\left(\frac{\pi}{3}\right)+\tan\left(\frac{\pi}{3}\right) = \frac{1}{2}+\sqrt{3}\]

Answer 29

tan(60)=opp side to the angle with measure 60/adj side to the angle with measure 60

Answer 30

I think once you know your unit circle triangles are really unnecessary. And there really is no arithmetic process needed.

Answer 31

Do you guys mind if we follow toms example cuz i think I understand better from that

Answer 32

and of course the hyp no matter angle we are labeling the triangle with respect to is the side opp to the 90 deg angle