# Tutor profile: Mark M.

## Questions

### Subject: Trigonometry

Find $$\theta,$$ if $$\sin( 3\theta - 15^\circ) = \cos(\theta + 25^\circ)$$

This problem involves the use of conversion properties of trigonometric functions. For example, we can convert a sine function into a cosine function as, $$\sin(X) = \cos(90^\circ - X)$$ This is because, $$\sin(X) = \cos(90^\circ - X) = \frac{side opposite to X}{hypotenuse}$$ So, given the equation: $$\sin( 3\theta - 15^\circ) = \cos(\theta + 25^\circ)$$ We need to find the value of $$\theta$$ We know that, $$\cos(90^\circ - X) = \sin(X)$$ Hence, $$\sin( 3\theta - 15^\circ) = \sin(90^\circ - (\theta + 25^\circ))$$ Therefore, $$3\theta - 15^\circ = 90^\circ - \theta - 25^\circ$$, Then, $$4\theta = 80^\circ$$, so $$\theta = 20^\circ$$

### Subject: Physics

Choose the right answer: A physics book rests on a table top. A gravitational force pulls down on the book. According to Newton's third law. The force that is equal to this gravitational force is: -the force the table exerts upward on the book. -the force the book exerts downward on the table. -the force the book exerts upward on the table. -the force the air pressure exerts down on the book.

The answer is: "the force the table exerts upward on the book.". As per Newton's third law which states that "For every action, there's a reaction that's equal in magnitude and opposite in direction", the force exerted on the table by the book downward (the weight of the book) has an equal reaction by the table on the book upward to make the book stationary.

### Subject: Algebra

Choose the correct answer: The degree of the polynomial $$p(x) = x(5x^7 + 2x^3 - 3x^2 + x)$$ is: -8 -7 -2 -1

The answer is '8'; the degree of the polynomial is determined by the highest power, and here the highest power is 8 since $$x$$ is multiplied by the whole bracket, so the product of the first term is $$5x^8$$.

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