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# Trigonometric Identities - University of Wisconsin–La … - cos to sin calculator

Trigonometric Identities
MTH 151
Reciprocal Identities Formulas for Negatives
1 (1)
csc t = sin t sin(-t) = - sin t (12)
1 (2) cos(-t) = cos t (13)
sin t = csc t
tan(-t) = - tan t (14)
1 (3)
sec t = cos t csc(-t) = - csc t (15)
1 (4) sec(-t) = sec t (16)
cos t = sec t cot(-t) = - cot t (17)
1 (5)
cot t = tan t
1 (6) Cofunction Formulas
tan t = cot t
Tangent and Cotangent sin - u = cos u (18)
sin t (7)
2
tan t = cos t cos 2 - u = sin u (19)
cot t = cos t (8) sec - u = csc u (20)
sin t 2
Pythagorean Identities csc - u = sec u (21)
sin2 t + cos2 t = 1 (9)
2
1 + cot2 t = csc2 t (10) tan 2 - u = cot u (22)
tan2 t + 1 = sec2 t (11) cot - u = tan u (23)
2
sin(u + v) = sin u cos v + cos u sin v (24)
cos(u + v) = cos u cos v - sin u sin v (25)
tan u + tan v (26)
tan(u + v) = 1 - tan u tan v
Subtraction Formulas
sin(u - v) = sin u cos v - cos u sin v (27)
cos(u - v) = cos u cos v + sin u sin v (28)
tan u - tan v (29)
tan(u - v) = 1 + tan u tan v
Double-Angle Formulas Half-Angle Formulas
sin 2u = 2 sin u cos u (30)
cos 2u = cos2 u - sin2 u (31) sin v = ? 1 - cos v (38)
cos 2u = 1 - 2 sin2 u (32)
22
cos 2u = 2 cos2 u - 1 (33) cos v = ? 1 + cos v (39)
22
tan 2u = 2 tan u (34) v = ? 1 - cos v (40)
1 - tan2 u tan 2 1 + cos v
Half-Angle Identities
sin2 u = 1 - cos 2u (35) Alternate Half-Angle Formulas
2
cos2 u = 1 + cos 2u (36) v = 1 - cos v (41)
2 tan 2 sin v
1 - cos 2u (37) v = sin v (42)
tan2 u = 1 + cos 2u tan 2 1 + cos v
Product-to-Sum Formulas
sin u cos v = 1 [sin(u + v) + sin(u - v)] (43)
2
cos u sin v = 1 [sin(u + v) - sin(u - v)] (44)
2
cos u cos v = 1 [cos(u + v) + cos(u - v)] (45)
2
sin u sin v = 1 [cos(u - v) - cos(u + v)] (46)
2
Sum-to-Product Formulas
sin a + sin b = 2 sin a + b cos a - b (47)
22
sin a - sin b = 2 cos a + b sin a - b (48)
22
cos a + cos b = 2 cos a + b cos a - b (49)
22
cos a - cos b = -2 sin a + b sin a - b (50)
22

What is cos sin equal to? Sin Cos formulas are based on the sides of the right-angled triangle. Sin and Cos are basic trigonometric functions along with tan function, in trigonometry. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse whereas the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

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