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14 Cards in this Set

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when performing arcsin, arccosine, or arctan there should always be ______ solutions in the domain 0 to 2pi, the calculator telling you only one.

Two. Always write two solutions when you perform arc functions. THEN interpret them to see if you need more.

To find the second solution in a sine period of 0 to 2 pi

subtract the first x value from pi


To find the second solution in a cosine period of 0 to 2 pi

subtract the first x value from 2 pi

Sketching the funciton in a given domain is useful because

you are able to see how many solutions you are supposed to get

To find the second solution in a tangent period of 0 to 2 pi...

add pi

(cosx)^2 is written as

cos^2(x) and likewise for any others

when cos = 0, tan is?

undefined because you can not divide by zero. This is what gives rise to asymptotes as tan=sin/cos

pythagorean identity

sin^2 x + cos^2 x = 1

When solving trigonometric equations, solve for the argument and then

calculate all other values in the domain. Be especially careful with the period. If the argument is of the form kx and not x then the period will be 2pi/k for cos and sin and pi/k for tan


Dividing sin^2 x + cos^2 x = 1 by sin^2 gives

1 + cot^2 x = csc^2 x

Dividing sin^2 x + cos^2 x = 1 by cos^2 gives

tan^2x + 1 = sec^2 x

CAST diagram tells you

which quadrants the trig function is positive in

A useful starting point when solving trig equations involving tan and also sin/cos is to change

tan x into sinx/cosx

Look out or hidden ____________

quadratics. When you will have, as an example, sin^2 x, sin x and a constant. Solve by factorizing or formula.