Trig Identities and Equations

Fundamental Identities

100

This is the reciprocal of sin(x).

What is csc(x)?

200

This expression will be equivalent to csc(40^o) using a cofunction identity.

What is sec(50^o)?

300

This expression will be equivalent to -sin(-30).

What is sin(30)?

400

These are the two relationships that tan(x) and cot(x) share.

What are cofunctions and reciprocals?

500

This is the type of symmetry that sec(x) has.

What is reflectional symmetry about the y-axis?

Pythagorean Identities

100

This is the sum of sin²(x) and cos²(x).

What is 1?

200

This is the equation of the unit circle(this is related trust).

What is x²+y²=1?

300

Why must the point (-0.8,0.6) lie on the unit circle?

(-0.8)²+(0.6)²=1

400

This expression is equivalent to (1+cos(x))(1-cos(x)) and only uses one sine or cosine function.

What is sin²(x)?

500

This is an expression equivalent to (1-cos²(x))/(1+tan²(x)) that contains only sine and/or cosine.

What is sin²(x)cos²(x) or (1/2)(sin²(2x))?

Sum/Difference Identities

100

This is the expansion of sin(x+y).

What is sin(x)cos(y)+cos(x)sin(y)?

200

This is the condensed formula for cos(x)cos(y)+sin(x)sin(y).

What is cos(x-y)?

300

This is the exact value of sin(7pi/12).

What is (√6+√2)/4?

400

This is the exact value of cos(pi/12).

What is (√6+√2)/4?

500

This is the exact value of (tan(30)+tan(60))/(1-tan(30)tan(60)).

What is DNE/undefined?

Double/Half Angle Identities

100

This is the amount of formulas that can be used to expand cos(2x).

What is 3?

200

This is the amount of formulas that can be used to expand tan(x/2) that include a square root symbol.

What is 1?

300

This is the condensed form of 2*(1/2)*√(3)/2 using a double angle identity.

What is sin(120)?

400

This is the exact value of cos(pi/8).

What is (√(2+√2))/2?

500

This is the condensed expression for sin(x)cos(x) such that only sin is present.

What is 1/2sin(2x)?

Trig Equations

100

These are the solutions to sin(x)=1 in the range [0,2pi).

What are pi/2 and 3pi/2?

200

These are the solutions to cos(2x)=1 in the range [0,2pi).

What are 0 and pi?

300

These are the solutions to tan(x)=1 in the range [0,2pi).

What are pi/4, 3pi/4, 5pi/4, and 7pi/4?

400

These are the solutions for 2sin(x)-1=0 (in radians).

What are π/6 + 2πk and 5π/6 + 2πk?

500

These are the solutions for 2cos²(x)=3-3sin(x) (in degrees).

What are 30^o+ 360^ok, 150^o + 360^ok, and 90^o + 360^ok.