Question

Please teach me to solve three of these equations through my calculator. Then I shall answer the other three questions by myself. If an answer is undefined, input DNE!!!sin(0)= _______ ;cos(0)=_______;tan(0)=_______ ;cot(0)=_________;sec(0)=_________;csc(0)=________;

Answer 1

Hello there. To solve this question, we'll have to remember some properties about the unit circle and trigonometric functions.

The unit circle is:

For any values in the circle, the x and y coordinates of the points are equal to the cosine and sine of the angle, respectively;

By definition, when x is equal to zero, sin(0) is 0, since the radius of the circle will be at the x-axis, in other words, there will be no height for the triangle formed.

By the same reason, cos(0) = 1, because it is the point where the circle touches x = 1.

To find the tangent, we can apply the formula:

`\tan (\alpha)=(\sin (\alpha))/(\cos (\alpha))`

And use the values we know

`\tan (0)=(\sin (0))/(\cos (0))=(0)/(1)=0`

The geometric interpretation for the tangent in the unit circle can be seen above, it touches the x-axis when the angle is zero, therefore it is also zero.