This week in pre-Calculus we learned all about Trigonometry and built upon what we had learned in math 10. I feel as though I really learned a lot in this unit from rotation angles to how to use the sine and cosine laws.

Terms to know:

• Rotation angle: formed between the initial arm and terminal arm. A counter clockwise rotation will result in a positive (+) angle whereas a clockwise rotation will result in a negative (-) angle.
• Initial Arm: The initial point in where you started measuring from. Your starting point of the arm.
• Terminal Arm: the area where the measurement of the angle stops. Your ending position of the arm.
• Reference Angle: Formed between the x-axis and the terminal arm.
• Co-terminal: Angles with the same terminal arm
• The CAST Rule: Starting in quadrant 4 and moving in a counter clockwise manner, will tell you which trigonometric ratios will be positive in the certain quadrants.

• Special Triangles: There are two special triangles , the 30°-60°-90° and the isosceles right triangle (45°-45°-90°), Since we know the sides of these triangles, we know their trigonometric ratios. If you come across any of these angles you will be able to refer to these two special triangles for your ratios instead of trying to calculate. Note: If one of the sides was multiplied by 2, you would need to do the same to the rest of them.

• Quadrantal angles: These are the angles where the terminal arm is located on the x or y-axis, ex. 0°, 90°, 180°, etc. r = 1, always.

Formulas To Know:

The new and improved SOH CAH TOA: *r = radius*

New and improved Pythagoras:

Sine Law: Works with any triangle

 (for calculating side length) OR (calculating angles)

Cosine Law: Works for all triangles, can re arrange to fit which parts of the triangle your are looking for

 (for calculating side length) OR  (calculating angles)

Example 1:

Q: Find what quadrants the terminal arm of the angles could lie.

 –> Quadrants: 2 and 4

• To find what possible quadrants a terminal arm could lie you use the CAST law
•  If we know that the tangent angle is negative then we know that it will have to lie in either quadrant 2 or 4. In quadrant one, all angles are positive, and in quadrant three, tangent is positive.

Example 2: Sine Law

Q:  to the nearest degree

• First, since we are trying to find the angle, we use the sine law formula that has the angles on the top and the side on the bottom of the fractions
• Next, take all the information you know and put it into the formula. Note: the lower case letters represent the sides, the sides are named after the angle that is opposite of it.
• If you take a look, you can see that one of the fractions has no information known about it, due to this we can take it out of the equation and use the other two fractions to help us find angle E. Now you rearrange the equation to isolate angle E. To do this you would multiply both sides by the denominator of the fraction that contains SinE; you would then need to get rid of the sin attached to the E, to do this you multiply the other side by the inverted sin.
• Next, solve and round your answer to the nearest degree.

Example 3: Cosine Law

Q: To the nearest tenth of a cm, find side a

• First, since we are trying to find one of the side lengths we would use the following formula: , since this is written in the form that we need it in, we would leave it the same.
• Next input all information you know about the triangle into the formula and the solve.
• Take that answer that you get in your calculator and square root it to find what the value of a is.