The document provides trigonometric values for 30°, 45°, and 60° angles without using a calculator. It lists the sine, cosine, and tangent values for 30° (1/2, √3/2, 1), 45° (√2/2, √2/2, 1), and 60° (√3/2, 1/2, √3). It also explains how to use trigonometric functions and reference angles to find the values of related angles, such as using the fact that sin 135° = sin 45° to determine that sin 135° = 1/√2.

1. Exact Values
For Higher you need to be able to calculate some trig values without a calculator.
To help us do this we need to learn the following triangles.
***These are not given in the formula sheet!!!
45o
30o
√2
2
1
√3
45o
60o
1
1
We use basic Trig (SOHCAHTOA) to find any angle above.
sin 30 = opp/adj ½
=

2. Associated Angles
We can also find angles related to
30, 45 and 60o
Examples
Find sin 135o
Step 1:
Draw the 4 quads and plot angle.
90
135o
Step 2:
Use "SATC" from S4 determine "+"
to
or "-"
0
180
Step 3:
Head towards the x axis to get related
angle
270
The angle is in Quad 2
Sine is +ve in quad 2
So the related angle will be +ve
135o
45o
180
so Sin 135 Sin 45
= +
1/√2
=