State both primary and general solutions in radians for each...

State both primary and general solutions (in radians) for each equation. 11. $\sin x + \cos x = 0 \approx -0.78^\circ$ 12. $4 \cos x = 3 \sec x$ 13. $\csc^2 x - 2 = 0 \pm 0.78^\circ$ 14. $\cos^2 x + \sin x = 1$ B. Exercises State general solutions (in radians) for each equation. 15. $\sin^2 x + 1 = \cos^2 x$ 16. $\cos^2 x - 2 \sin x = 1$ 17. $3 \sin^2 x = \cos^2 x$ 18. $2 \cos x - \sin 2x = 0$

Transcript

00:01 One way to answer a lot of equations like this is graphically, or at least to check your answers if you are doing it by hand.

00:07 I'm going to do all of the ones in radiance first.

00:15 So let's do a, here's what i mean by this if you're not familiar.

00:20 You can do the square to 2, sine 3x minus 1.

00:28 When is it equal to 0? well, that's when it crosses the x -axis at pi over 12 is the first one.

00:48 B has x, so that's in radiance.

00:52 So that's negative 2 cosine, or in degree mode, 2x.

01:03 And then if it's equal to square to 3, you can just subtract the square root of 3, and then you're equal to 0.

01:10 Look at the x -axis.

01:11 That's 5 pi over 12 for the smallest non -negative answer.

01:19 Again, 5 pi over 12.

01:27 C and d i'll come back to let's go to e in essence there in radiance.

01:38 So e is 2 square root 3, sine of x over 2, and then we'll subtract 3 so that we're equal to 0 and it's 2 pi over 3.

02:00 F is 2 square root 3 times the cosine of x over 2, and then we'll subtract 3, and then we will would add 3 so that we're equal to 0, 5 pi over 3.

02:27 Now i'll do i and j.

02:31 For i, it's sine 2 x.

02:36 And then if it's equal to 2, cosine squared x, we'll just subtract 2.

02:41 Now the way you do this in a calculator is cosine x squared.

02:49 You're squaring the cosine.

02:52 And we're subtracting that so that we're equal to 0 and that happens at pi over 4.

03:00 J is 3 cosine squared of x over 2...