Unit 2 Earth Materials Lab 2 3 Igneous Rock Identification
More important identities
You don't have to know all the identities off the top of your head. But these you should.
Defining relations for tangent, cotangent, secant, and cosecant in terms of sine and cosine.
|tan t = |sin t | |cot t = |1 |= |cos t |
| |[pic] | | |[pic] | |[pic] |
| |cos t | | |tan t | |sin t |
|sec t = |1 | |csc t = |1 | | |
| |[pic] | | |[pic] | | |
| |cos t | | |sin t | | |
The Pythagorean formula for sines and cosines. sin2 t + cos2 t = 1
Identities expressing trig functions in terms of their complements cos t = sin([pic]/2 – t) sin t = cos([pic]/2 – t) cot t = tan([pic]/2 – t) tan t = cot([pic]/2 – t) csc t = sec([pic]/2 – t) sec t = csc([pic]/2 – t)
Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2[pic] while tangent and cotangent have period[pic]. sin (t + 2[pic]) = sin t cos (t + 2[pic]) = cos t tan (t + [pic]) = tan t
Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions. sin –t = –sin t cos –t = cos t tan –t = –tan t
Sum formulas for sine and cosine sin (s + t) = sin s cos t + cos s sin t cos (s + t) = cos s cos t – sin s sin t
Double angle formulas for sine and cosine sin 2t = 2 sin t cos t cos 2t = cos2 t – sin2 t = 2 cos2 t – 1 = 1 – 2 sin2 t
Less important identities
You should know that there are these identities, but they are not as important as those mentioned above. They can all be derived from those above, but sometimes it takes a bit of work to do so.
The Pythagorean formula for tangents and secants. sec2 t = 1 + tan2 t
Identities expressing trig functions in terms of their supplements
You don't have to know all the identities off the top of your head. But these you should.
Defining relations for tangent, cotangent, secant, and cosecant in terms of sine and cosine.
|tan t = |sin t | |cot t = |1 |= |cos t |
| |[pic] | | |[pic] | |[pic] |
| |cos t | | |tan t | |sin t |
|sec t = |1 | |csc t = |1 | | |
| |[pic] | | |[pic] | | |
| |cos t | | |sin t | | |
The Pythagorean formula for sines and cosines. sin2 t + cos2 t = 1
Identities expressing trig functions in terms of their complements cos t = sin([pic]/2 – t) sin t = cos([pic]/2 – t) cot t = tan([pic]/2 – t) tan t = cot([pic]/2 – t) csc t = sec([pic]/2 – t) sec t = csc([pic]/2 – t)
Periodicity of trig functions. Sine, cosine, secant, and cosecant have period 2[pic] while tangent and cotangent have period[pic]. sin (t + 2[pic]) = sin t cos (t + 2[pic]) = cos t tan (t + [pic]) = tan t
Identities for negative angles. Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions. sin –t = –sin t cos –t = cos t tan –t = –tan t
Sum formulas for sine and cosine sin (s + t) = sin s cos t + cos s sin t cos (s + t) = cos s cos t – sin s sin t
Double angle formulas for sine and cosine sin 2t = 2 sin t cos t cos 2t = cos2 t – sin2 t = 2 cos2 t – 1 = 1 – 2 sin2 t
Less important identities
You should know that there are these identities, but they are not as important as those mentioned above. They can all be derived from those above, but sometimes it takes a bit of work to do so.
The Pythagorean formula for tangents and secants. sec2 t = 1 + tan2 t
Identities expressing trig functions in terms of their supplements