trig identities

basic identities

What is the reciprocal of sin(x)?

csc(x)

What is the reciprocal of cos(x)?

sec(x)

What is the reciprocal of tan(x)?

cot(x)

What is the reciprocal of csc(x)?

sin(x)

What is the reciprocal of sec(x)?

cos(x)

What is the reciprocal of cot(x)?

tan(x)

What is the quotient identity for tan(x)?

tan(x) = sin(x)/cos(x)

What is the quotient identity for cot(x)?

cot(x) = cos(x)/sin(x)

What is the fundamental Pythagorean identity?

sin²(x) + cos²(x) = 1

What identity comes from dividing the fundamental identity by cos²(x)?

tan²(x) + 1 = sec²(x)

What identity comes from dividing the fundamental identity by sin²(x)?

1 + cot²(x) = csc²(x)

What is sin(-x)?

–sin(x)

What is cos(-x)?

cos(x)

What is tan(-x)?

–tan(x)

Which trig functions are odd?

sin(x)

Which trig functions are even?

cos(x)

What is sec²(x) - 1 equal to?

tan²(x)

What is csc²(x) - cot²(x) equal to?

1

What is 1 - sin²(x) equal to?

cos²(x)

What is 1 - cos²(x) equal to?

sin²(x)

What is the identity for tan²(x) + 1?

sec²(x)

What is the identity for 1 + cot²(x)?

csc²(x)

How can you express cos²(x) in terms of sin²(x)?

cos²(x) = 1 - sin²(x)

How can you express sin²(x) in terms of cos²(x)?

sin²(x) = 1 - cos²(x)