Question

Find the value of $2\sin 30^\circ + \cos 0^\circ + 3\sin 90^\circ$.

Answer 1

Here, we will first simplify the given equation using the sine value, $\sin 30^\circ = \dfrac{1}{2}$, cosine value $\cos 0^\circ = 1$, and sine value $\sin 90^\circ = 1$ in the given expression to find the required value.

Complete step by step answer:

We are given that the equation is $2\sin 30^\circ + \cos 0^\circ + 3\sin 90^\circ$.
We will now use the sine value, $\sin 30^\circ = \dfrac{1}{2}$ in the given equation, we get

$$\Rightarrow 2 \times \dfrac{1}{2} + \cos 0^\circ + 3\sin 90^\circ \\\ \Rightarrow 1 + \cos 0^\circ + 3\sin 90^\circ \\\$$

Using the cosine value, $\cos 0^\circ = 1$ in the above equation, we get

$$\Rightarrow 1 + 1 + 3\sin 90^\circ \\\ \Rightarrow 2 + 3\sin 90^\circ \\\$$

Using the sine value, that is, $\sin 90^\circ = 1$ in the above equation, we get

$$\Rightarrow 2 + 3 \times 1 \\\ \Rightarrow 2 + 3 \\\ \Rightarrow 5 \\\$$

Thus, the value of the given equation is $5$.

Note: The key concept is to have good understanding of the basic trigonometric values and learn how to use the values from trigonometric tables. Students should have grasp of trigonometric values, for simplifying the given equation. The common mistake is students write $\cos 0^\circ$ equal to 0 instead of 1, which is a wrong. We will follow the BODMAS rule here, so do not add before multiplying or else the answer will be wrong.