Further Trigonometry

Question 1

Recap right angle trig:

Answer 1

SOH CAH TOA

Question 2

Explain why Sin (90-x)=Cos(x) and

Cos(90-x)=Sin(x).

Answer 2

In a right angle triangle, the two unknown angles would be (x) and (90-x). Sin (x) would equal b/c, and sin (90-x)=a/c if you imagine triangle ACB, with C the right angle. Cos(x) would equal a/c also, and Cos (90-x) would equal b/c also, proving the equations are equal.

Question 3

State the Tangent Ratio and the proof for it.

Answer 3

Tan(x)=Sin(x)/Cos(x)=b/a

Tan(x)=b/a
Sin(x)=b/c
Cos(x)=a/c
Sin(x)/Cos(x)=b/c//a/c=b/a=Tan(x)

Question 4

How do you remember which of Sin, Cos and Tan are positive in the 1st, 2nd, 3rd and fourth quadrants?

Answer 4

All
Stations
To
Central

Question 5

What is the Sin Rule?

Answer 5

Sin(A)/a=Sin(B)/b=Sin(C)/c

a/Sin(A)=b/Sin(B)=c/Sin(C)

Question 6

What is the Cosine Rule?

Answer 6

a^2=b^2+c^2-2bcCos(A)

Cos(A)=(b^2+c^2-a^2)/(2bc)

Question 7

How do you find the area of a triangle using trigonometry?

Answer 7

A=(1/2)abSin(C)