Inverse Trig Functions
arcsin(-sqrt3/2).
What is -pi/3?
The simplified form of sin(-x) due to the even-odd identities.
What is -sin(x)?
The simplified form of sin(3x)cos(2x)+sin(2x)cos(3x).
What is sin(5x)?
The solution(s) to -2cos(x)=-sqrt2 between (0, 2pi].
What are pi/4 and 7pi/4?
The component form of a vector with initial point (1,0) and terminal point (5,-4).
What is <4, -4>?
The angle measure B in right triangle with c=10 and b=5.
What is 30 degrees?
The process for proving a trig identity.
What is begin with either the right side or the left side and write equivalent expressions until you obtain the other side?
The exact value of tan(7pi/12), found by using sum and difference identities.
What is (sqrt(3)+1)/(sqrt(3)-1)?
The solution(s) to 4cost=2 between (0, 2pi].
What are pi/3 and 5pi/3?
The direction and magnitude of the vector <sqrt2/2, sqrt2/2>.
What are pi/4 and 1, respectively?
The domain and range of the arccos function.
What are [-1,1] and [0, pi], respectively?
The simplified form of sin(x)cos(x)csc(x).
What is cos(x)?
The exact value of 3sin(pi/8), found by using half angle identities.
What is (3/2)sqrt(2-sqrt(2))?
The solution(s) to cos^3(t)=cos(t) between (0, 2pi].
What are pi/2, pi, 3pi/2, and 2pi?
The direction and magnitude of the vector 9sqrt(3)i-9j.
What are 11pi/6 and 18, respectively?
arcsin(sin(3pi/4)).
What is pi/4?
The three Pythagorean identities.
What are cos^2(x)+sin^2(x)=1, sec^2(x)=1+tan^2(x), and csc^2(x)=1+cot^2(x)?
The exact value of cos(75 degrees)*sin(15 degrees) using the appropriate trig identity.
What is (2-sqrt(3))/4?
The solution(s) to 2sin^2(x)-3sin(x)+1=0 between (0, 2pi].
What are pi/6, pi/2, and 5pi/6?
The simplified component form of a vector with magnitude 3 and direction 270 degrees.
What is <0, -3>?
cos(arcsin(3/5)).
What is 4/5?
The factored form of sec^2(x)+3tanx+1.
What is (tan(x)+2)(tan(x)+1))?
If sin(x)=-4/5 and x is in quadrant 3, this is the exact value of cos(x/2).
What is -sqrt(5)/5?
The solution(s) to tan^5(t)=tan(t) between (0, 2pi].
What are pi/4, 3pi/4, pi, 5pi/4, 7pi/4, and 2pi?
The simplified component form of a vector with magnitude 2 and direction 150 degrees.
What is <-sqrt(3), 1>?