Define and evaluate the trigonometric functions of tangent, cosecant, secant, and cotangent.
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Below are six different trigonometric ratios, all noted on the unit circle.
“$${\mathrm{sec}\theta}$$” is “secant of theta”
“$${\mathrm{cosec}\theta}$$” is “cosecant of theta” (also can be written as $${\mathrm{csc}\theta}$$)
“$${\mathrm{cot}\theta}$$” is “cotangent of theta”
What is the relationship between the sine, cosine, and tangent and these three new trigonometric functions?
Reciprocal Trig Functions on the Unit Circle by mathsurgery.wikispaces is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed Feb. 26, 2018, 1 p.m..
Evaluate the following expressions:
a. $${\mathrm{csc}(30^\circ)}$$
b. $${\mathrm{cot}(135^\circ)}$$
c. $${\frac{\mathrm{cos}(45^\circ)}{\mathrm{sec}(60^\circ)}}$$
d. $${-\mathrm{cos}(-60^\circ)}$$
The image below shows where the values of sine and cosine are positive and negative. Fill out a similar image for cosecant, secant, tangent, and cotangent.
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Evaluate:
$${\mathrm{tan}0^\circ}$$
$${\mathrm{cot}45^\circ}$$
$${\mathrm{csc}90^\circ}$$
Where is the value of $${\mathrm{sec}\theta}$$ undefined?