Six Trig Functions

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Unit 2-Functions

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tan (π/2 - u) = cot u

cos (-u) = cos u

sin (π/2 - u) = cos u

1 + cot ^2 u = csc^2 u

1 =tan^2 u = sec^2 u

tan u = sin u/ cos u

cot u = cos u/ sin u

Standard form

a^2 = b^2 + c^2 - 2bc cos A b^2 = a^2 + b^2 - 2ab cos B c^2 = a^2 + b^2 - 2ab cos C

Standard Form

a^2 = b^2 + c^2 - 2bc cos A b^2 = a^2 + c^2 - 2ac cos B c^2 = a^2 + b^2 - 2ab cos C

sin u = cos(π/2 -u)

sec u = csc u (π/2-u)

csc u = sec(π/2 - u)

cot u = tan (π/2 -u)

cos u = sin u (π/2 - u)

cot u = cos u/sin u

tan u = sin u/cos u

The graph of sec (θ) looks like the csc (θ) graph

It too has a "u" shaped but starts half on the negative x axis and positive y axis and half on the positive x axis and positive y axis. Then back to the positive x axis and negative y axis "u" and back up to the positive x and y axis "u".

The graph of csc (θ) looks "u" shaped

The graph starts on the positive side of the x and y axis makes a "u" shape, then it starts again at the bottom of the positive x axis and negative y axis to make another "u".

The graph of cot (θ) looks like the tan (θ)

It begins on the negative x and y axis moves toward the positive y axis and moves slightly to the left and up. This continues the same way the tan (θ) graph.

The graph of cos (θ) looks like sin (θ)

The main difference between sin (θ) and cos (θ) is that cos (θ) does not cross (0,0)

Graph of tan (θ) has many curved lines

It starts toward the bottom of the negative side of the x and y axis, moves up toward the positive y side and curves slightly to the left up into the positive y axis. This line continues throughout the rest of the graph over and over.

The graph of sin (θ) looks like a wave

It begins on the negative side of the x axis and positive side of the y axis, then it falls under the x axis. It crosses (0,0) and moves back up on the positive sides of the x and y axis then falls to the negative side of the y axis and back up.

cos (θ) = x/1 = x

tan (θ) = y/x

cot (θ) = x/y

csc (θ) = 1/y

sec (θ) = 1/cos x

sin (θ) = y/1 = y

csc (θ) = 1/sin (θ)

cos (θ) = 1/sec (θ)

tan (θ) = 1/cot (θ)

sin (θ) = 1/csc (θ)

cot (θ) = 1/tan (θ)

Subtopic

sec (θ) = 1/cos (θ)

Trigonometry Functions

cot(θ)

csc (θ)

sec(θ)

cos(θ)

tan(θ)

sin(θ)