Question

Can anyone help me understand sin, tan, cos and their reciprocals ?

Answer 1

sine, cosine, and tangent are all just ratio in relation to a specific angle

Answer 2

we'll call the specific angle theta
\[{t heta} = \theta\]

now, for trig

\[\sin(\theta)= \frac{opposite side }{hypothenuse}\]

\[\cos(\theta)= \frac{adjacent side }{hypothenuse}\]


\[\tan(\theta)= \frac{opposite side }{adjacent side}\]

Answer 3

do you understand it so far?

Answer 4

I know all of that but I always get confused when I just see a right triangle. A lot of times I don't know what I should be looking for. Is there any rule for when I need to specifically use one of those ?

Answer 5

using the acronym
SOH CAH TOA helps in memorizing the the properties of sine cosine and tangent

Answer 6

ok here's an example

say i give you this

Answer 7

assume that is a right triangle

Answer 8

and the problem is to find the value of x

Answer 9

there are no specific rules to determine whether or not to use sine,cosine, or tangent

just looking at the picture, we know that the adjacent side is given and we want to find the hypothenuse

so going back to SOH CAH TOA

we determine which one of the three, deals with the adjacent side and hypothenuse

Answer 10

which one do you think it would be?

Answer 11

cos ?

Answer 12

@completeidiot

Answer 13

yes
you would use cosine

so you set up the equation

\[\cos(30 ^\circ)= \frac{5}{x}\]

Answer 14

and solve for x
\[x=\frac{5}{\cos(30^\circ)}\]

Answer 15

by dividing ? Is it 0.866 ?