If cos 26° = k, express the following in terms of k: 3.2.1 sin 26°

The fundamental trigonometric identity is $\sin^2 \theta + \cos^2 \theta = 1$.
For $\theta = 26^\circ$, this becomes:

$$\sin^2 26^\circ + \cos^2 26^\circ = 1$$

We are given that $\cos 26^\circ = k$. Substitute this into the identity:

$$\sin^2 26^\circ + (k)^2 = 1$$ $$\sin^2 26^\circ + k^2 = 1$$

Subtract $k^2$ from both sides:

$$\sin^2 26^\circ = 1 - k^2$$

Take the square root of both sides. Since $26^\circ$ is in the first quadrant, $\sin 26^\circ$ is positive.

$$\sin 26^\circ = \sqrt{1 - k^2}$$

The expression for $\sin 26^\circ$ in terms of $k$ is:

$$\sqrt{1 - k^2}$$