The focus of this week is Trigonometry.

Important terms:

Initial Arm: The arm of an angle that lies on the x-axis.

Standard position: When the initial arm is on the positive x-axis.

Terminal arm: The terminal arm is the other arm, it can be anywhere and it determines  the angle.

Refrence angle: The closest angle between the Terminal arm and the x-axis.

Coterminal: Standard angle that shares the same terminal arm as another angle.

Rotation Angle: The angle from the initial arm to the terminal arm.

Ex: 

Sine Law:

The sine law can be used to find an angle or length of a side. To find the length of a side use the top formula, to find an angle, use the bottom formula (the reciprocal). You can only use the sine law if you have both the angle and side of one of the fractions, such as angle A and side a, or angle B and side b, etc.

Cosine Law:

The cosine law can be used instead of the sine law, if there are no fractions that have a value for both the angle and the length of the side.

You can tell if you need to use sine law or cosine Law just by looking at a triangle. If there is an angle in the triangle with a side value across from it, you can use sine law. But, if the angles don’t have a side measurement across from them, you will have to use cosine law.

In this example, you can use sine law:

In this example, you have to use cosine law:

The CAST rule:

The cast rule is an easy way to remember, which trigometric ratios are positive and which are negative in every quadrant.

Updated SOH CAH TOA:

In this unit SOH CAH TOA is updated to SYR CXR and TYX. When given a (x,y) point on the terminal arm, we can determine the refrence angle using the updated SOH CAH TOA.