Precalc: Inverse Trig, Identities, Sum/Double, Law of Sines/Cosines

Inverse Trig

100

Evaluate: 

arcsin(sin(-\frac{pi}{4}))

-\frac{pi}{4}

150

Evaluate: 

arccos(cos(\frac{8pi}{7}))

\frac{6pi}{7}

200

Evaluate in terms of 'x':

sec(arcsin(\frac{3}{x}))

\frac{|x|}{\sqrt{x^2-9}

250

State the domain and range of 

f(x)=csc(arctan(4x))

D:(\-infty,0)\cup(0,\infty)

R:(\-infty,-1)\cup(1,\infty)

Note: The domain does not exclude 0 due to the arctan function, but instead because the cosecant function is undefined when the input is 0.  csc(arctan(4*0))=csc(0)="undefined" 

Law of Sines/ Cosines

100

How many triangles can be formed given 

\angleA=20^(circ), a=5, b=12

Two

150

How many triangles can be formed given 

\angleA=150^(circ), a=4, b=8

Zero (obtuse!)

200

Find the area of a triangle with sides  6, 10, 11 rounded to three decimals. 

29.765

250

Yogi wants to measure a tree. He measures the angle of elevation to the tree from where he is standing to be  78^(circ) . He walks forward 7 feet and measures the angle to now be  82^(circ) . What is the height of the tree to three decimals?

97.201 feet

Double Angle

100

Given  sin\theta=7/10, cot\theta>0 evaluate  cos(2\theta) 

\frac{1}{50}

150

Evaluate  sin[2cos^-1(-3/5)] 

 -24/25 

200

Given  sec\theta=4 , csc\theta <0 evaluate  tan(2\theta) 

 sqrt15/7 

250

Given  tan\theta=\frac{4}{3}, sin\theta<0 evaluate: 

sin(4\theta)

-336/625

Sum and Diff

100

Evaluate  cos((5pi)/12) 

 (sqrt6-sqrt2)/4 

150

Evaluate  sin(pi/9)cos(pi/18)+cos(pi/9)sin(pi/18) 

 1/2 

200

Given   cot(a)=5/12, sin(a)<0 ; cos(b)=3/5, sin(b)<0 evaluate  sec(a-b) 

 65/33 

250

Evaluate  sin[arccos(\frac{5}{13})+arcsin(\frac{12}{13})] 

 

\frac{120}{169}