# How do you solve #\cos 2x = - 0.9#?

Use the inverse cosine.

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the equation (\cos 2x = -0.9), follow these steps:

- Use the double-angle identity for cosine: (\cos 2x = 2\cos^2 x - 1).
- Substitute (-0.9) for (\cos 2x): (2\cos^2 x - 1 = -0.9).
- Rearrange the equation: (2\cos^2 x = -0.9 + 1).
- Simplify: (2\cos^2 x = 0.1).
- Divide both sides by 2: (\cos^2 x = 0.05).
- Take the square root of both sides: (\cos x = \pm \sqrt{0.05}).
- Calculate the square root of (0.05).
- Since cosine can be both positive and negative, we have two cases: a. (\cos x = \sqrt{0.05}) b. (\cos x = -\sqrt{0.05}).
- Use the inverse cosine function to find the values of (x): a. For (\cos x = \sqrt{0.05}), (x = \arccos(\sqrt{0.05}) + 2\pi n) and (x = -\arccos(\sqrt{0.05}) + 2\pi n). b. For (\cos x = -\sqrt{0.05}), (x = \arccos(-\sqrt{0.05}) + 2\pi n) and (x = -\arccos(-\sqrt{0.05}) + 2\pi n).
- Calculate the numerical values of (x) using a calculator or computer software.
- Include (2\pi n) to account for all possible solutions, where (n) is an integer.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7