Trigonometry

Question 1

What is the abriviation for remembering the formulas of Sin, Cos and Tan? What does each letter stand for?

Answer 1

Soh→Cah→Toa

Sin= Opposite/ Hypotenuse→Cos= Ajacent/Hypotenuse→Tan= Opposite/Ajacent

Question 2

What are the 3 sides of the right angle triangle labeled as?

Answer 2

Hypotenuse: The diagonal line

Ajacent: The line beside the reference angle

Opposite: The remaining side

Question 3

What are the names of the 3 Primary Trig Ratios?

Answer 3

1) Sine (sin)
2) Cosine (cos)
3) Tangent (tan)

Question 4

Which parts of a triangle are labeled with:

a) Capital letters
b) Lowercase letters

Answer 4

a) Angles
b) Sides

Question 5

How do you find the labels for each side?

Answer 5

Each side length is opposite to its angle

Example: Side a is opposite to angle A

Question 6

What does it mean to solve for a triangle?

Answer 6

Find the missing side lengths and angles based on the given information

Question 7

When given 2 of the side lengths of a right triangle, how do you find the 3rd side length?

Answer 7

Pythagorean Theroem

a²+ b²= c²

*a and b are the legs and c is the hypotenuse*

Question 8

When given 2 angles of a triangle, how do you find the 3rd angle?

Answer 8

*All angles of a triangle add up to 180º*

Subtract the 2 given angles from 180° and the answer is the value of the 3rd angle

Question 9

When given 2 angles, and 1 side length of a right triangle, how do you solve?

Answer 9

Step 1) Find the 3rd angle

Step 2) Write your primary trig ratio (Sin, Cos or Tan) with the reference angle of your choice

sin25º

Step 2) Write the unknown value divided by the given side length in the order that follows the rules of your primary trig ratioratio

sin25°= a/12

Step 4) Cross multiply; Write the variable and move the number on the bottom of the fraction and multiply it by the trig ratio and the angle

a= 12 sin25º

Step 5) Enter into a calculator and write your answer

a= 5.1 cm

Question 10

When looking for an angle in a right triangle, what must you do to the primary trig ratios?

Answer 10

Use the inverse.

Example: Sin ^-1

*USE 2ND BUTTON, THEN TRIG RATIO ON YOUR CALCULATOR*

Question 11

Angle of Elevation

Answer 11

Question 12

Angle of Depression

Answer 12

Question 13

What is the Sin Law?

Answer 13

Using a primary trig ratio and an angle variable divided by a side length variable; and vice versa

Example: a/ SinA and SinA/a

Question 14

When can you use the Sin Law?

Answer 14

When you have a pair (Side length and opposite angle) and one more fact

Question 15

When do you use the Cosine Law?

Answer 15

When you know all 3 side lengths or 2 sides and an angle

Question 16

What are the 3 Cosine Law Formulas?

Answer 16

1) c²= a²+ b²- 2abCosC
2) b²=a²+c²- 2acCosB
3) a²= b²+c²-2bcCosA

Question 17

When do you use…

a) The Primary Trig Ratios
b) The Cosine/ Sin Law

Answer 17

a) Finding the parts of a right triangle
b) Finding the parts of any other triangle