Question

Explain how you evaluate the six trigonometric functions of the angle O

Answer 1

\[\sin\theta=\frac{\text{opposite side}}{\text{hypotenuse}}\]
\[\cos\theta=\frac{\text{adjacent side}}{\text{hypotenuse}}\]
\[\tan\theta=\frac{\text{opposite side}}{\text{adjacent side}}\]

Answer 2

\[\csc\theta=\frac1{\sin\theta}=\frac{\text{hypotenuse}}{\text{opposite side}}\]
\[\sec\theta=\frac1{\cos\theta}=\frac{\text{hypotenuse}}{\text{adjacent side}}\]
\[\cot\theta=\frac1{\tan\theta}=\frac{\text{adjacent side}}{\text{opposite side}}\]

Answer 3

to work out the adjacent side, you can use Pythagorean theorem

Answer 4

how do i do the pythagorean theorem on my calculator?

Answer 5

the Pythagorean theorem says that ; for a right angled triangle, the sum of the squares of the shorter sides equals the square of the hypotenuse(longest side)

\[a^2+b^2=c^2\]

you have the length of one of the shorter side (say a), and the hypotenuse (c)

sub in and solve for b

Answer 6

[a calculator isn't much help for this bit ]

Answer 7

wait but what do i do with the square root?

Answer 8

you should get\[3^2+b^2=(3\sqrt2)^2\]

Answer 9

to simplify the righthand side (3√2)^2 = 3√2 x 3√2 =(3 x 3) x (√2 x √2)

Answer 10

can you simplify √2 x √2 ?

Answer 11

no

Answer 12

\[√X \times√X =√X^2=X\]

Answer 13

oh so then yes

Answer 14

so what does the right hand side simplify to?

Answer 15

gimmie 5 min plz

Answer 16

ok

Answer 17

im back sorry

Answer 18

so have you simplified (3√2)^2 ?

Answer 19

not quite