I’m weaker when trig questions involve identities can someone list the steps of solving this
0<x<90 and 2sin^2-1=0, then x=
the answer is 45 degrees
Do you mean 2sin^2x-1=0?
Add one to both sides of the equation.
Divide both sides by 2.
Sin^2(x) = 1/2
Sin(x) = 1/sqrt(2)
If you don’t recognize it from there, put it in the calculator, make sure you’re in degree mode, and hit inverse-sine
(But, memorize your 30-60-90 and 45-45-90 triangles for the test if you can.)
yes
I have another question.
if b is not equal to c, what are the values of a that make the inequality true?
ab-ac / 2b-2c <0
A) 2 only
B) 1/2 only
C) -1/2 only
D) all positive real numbers
E) all negative numbers
Factor out the expression (b - c) from the numerator and denominator of the fraction. Now do you see it?
a(b-c) / 2(b-c)
Cancel out (b-c), so left with:
a/2<0
Solve for a:
2(a/2)< 2(0)
So a<0 so the answer is all negative numbers? I have no clue, could you tell me if this is right?
Yes, the answer a < 0 is correct. The inequality (ab-ac)/(2b-2c) < 0 is true if and only if a/2 < 0, which is true if and only if a < 0.
In general, you have to be careful when dividing by unknown expressions, since the sign matters. For example, if you had been solving the inequality
a(b-c) < 2(b-c)
where a, b, c are unknowns and b ≠ c, then “dividing” both sides of the inequality by b-c doesn’t necessarily work since we don’t know if b-c is positive or negative. For example if b-c = -1, then we have -a < -2, but dividing both sides by -1 without changing anything else gives us a < 2, which is not equivalent.