Tips For Learning Trig Rules. Reciprocal Rules Learn:
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Transcript of Tips For Learning Trig Rules. Reciprocal Rules Learn:
![Page 1: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/1.jpg)
Tips For LearningTrig Rules
![Page 2: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/2.jpg)
Reciprocal Rules
Learn:
xx sec1cos xx cos
1sec
xx csc1sin x
xsin1csc
xx cot1tan
xx tan1cot
xxx cos
sintan xxx
sincoscot
![Page 3: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/3.jpg)
Pythagorean Identities
xx
x
x
x2cos
12cos
2sin2cos
2cos
1. Learn
2. Derive the others by dividing.
12sin2cos xx
is xx 2sec2tan1
xx
x
x
x2sin
12sin
2sin2sin
2cos is xx 2csc12cot
![Page 4: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/4.jpg)
Co-Function Rules
Remember that cofunction rules come from complementary angles (meaning they sum to 90o or π/2).
Therefore trig(x) = co-trig(π/2 – x). This works for any of the co---- functions.
Example: csc(x) = sec(π/2 – x)
![Page 5: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/5.jpg)
Odd – Even Functions
Recall:Even functions have f(-x) = f(x). (Symmetry about the y-axis)
Odd functions have f(-x) = -f(x) (Symmetry about the origin)
Remember:cos and sec are the only even functions. All others are odd.
Therefore:
cos(-x) = cos(x) and sec(-x) = sec(x)For all other functions follow the pattern:sin(-x) = -sin(x) tan(-x) = -tan(x) etc
![Page 6: Tips For Learning Trig Rules. Reciprocal Rules Learn:](https://reader036.fdocuments.us/reader036/viewer/2022072011/56649e3f5503460f94b2fb68/html5/thumbnails/6.jpg)
General Principles
1. If you see squares such as cos2x, sin2x, tan2x think Pythagorean Identities.
2. If you have tan and cot mixed with sin and cos, use the tan x = sin x / cos x rules.
3. If there are negatives in the angle such as sec(-x), use odd/even rules.
4. If there are π/2 – x or 90o – x in the angle, use cofunction rules.