Trigonometry

Question 1

How do we solve an equation involving sin2x and cos2x?

Answer 1

Replace sin2x with 2sinxcox (from formula sheet) then solve by using HCF (if RHS=0)

Replace cos2x with 2cos^2x^-1 (if other term in equation is cos) or 1-2sin^2x (if other is sin. Then create quadratic in sin/cos and trinomial solve by factorising.

Question 2

How can you find the other two trig values if you’re given one?

i.e. sin+cos if given tanx

Answer 2

Make a right-angled triangle then label 2 sides from the values given in the question. Then use Pythagoras to work out length of 3rd side and create other trig identities from all 3 sides.

Question 3

How do you bring a trig answer into range 0-360* if your calculator gives you a negative answer?

Answer 3

Add 360* to the answer.

Question 4

What do both sin^-1 (+ve) answers add up to?

Answer 4

Both add up to 180*

Question 5

What do both cos^-1 (all) answers add up to?

Answer 5

Both add up to 360*

Question 6

What do both sin^-1 (-ve) answers add up to?

Answer 6

Both add up to 540*

Question 7

What do both tan^-1 (all) answers add up to?

Answer 7

Answers are +- 180* apart.

Question 8

How do you convert degrees to radians?

Answer 8

x Pi/180 or divide by 180/Pi

Question 9

How do you convert the angle a line makes with the positive direction of x-axis into a gradient?

Answer 9

m=tan(theta)

Question 10

How do you convert radians to degrees?

Answer 10

x 180/Pi or divide by Pi/180

Question 11

How can you work out the angle a line makes with the positive direction of the x-axis?

Answer 11

Find the gradient of the line then do tan^-1(gradient)

Question 12

When will your calculator give you a negative angle answer when you are trying to find the solutions to a trig equation?

Answer 12

When finding sin^-1 or tan^-1 of a negative number.

Question 13

What does a CAST diagram show?

Answer 13

Provides a method to find multiple solutions to trigonometric equations. It indicates the quadrants in which the trigonometric functions are positive.

Question 14

What is the first thing you must do when starting a paper for the first time (non-calculator especially)?

Answer 14

The quadrants where positive trig values lie, exact value triangles.

Question 15

What is a radian? And give an example of a degrees to radians conversion.

Answer 15

A unit of measuring angles equivalent to 57.3* (180/Pi).

Pi=180*
Pi/2=90*
2Pi=360*