Sin (105) = sin (15+90)= cos 15- ℎ ℎ

Explanation:
sin(105) = sin (60+45) because sin (a +b)= sin a • cos b+ cos a• sin b

Therefore,

sin 105= sin (60+45) = sin 60• cos 45 + cos 60 • sin 45 =

The picture below is your answer.

3 0

2 years ago

Stephen is a shy 10-year-old who rarely contributes in class by sharing his opinions on topics. Since the _____ in the United St

Rom4ik [11]

Teachers?

I think that this is right.

5 0

2 years ago

The graph of x^2=-2+y+5cosy is shown for y=11

erik [133]

(a)

We have been given an equation $x^{2}=-2+y+5cosy$ . Upon taking derivative of this equation with respect to x on both the sides, we get:

$2x=0+\frac{dy}{dx}+5(-siny)\frac{dy}{dx}\\2x=(1-5siny)\frac{dy}{dx}\Rightarrow \frac{dy}{dx}=\frac{2x}{1-5siny}$

(b)

In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

$\text{Slope}=\frac{dy}{dx}=\frac{2(3)}{1-5sin(11)}=1$

Therefore, equation of tangent line is:

$y-y_{1}=m(x-x_{1})\Rightarrow y-11=1(x-3)\\y-11=x-3\\y=x+8$

(c)

We know that slope of tangent is given as $\frac{dy}{dx}=\frac{2x}{1-5siny}$ . The tangent will be vertical when denominator of slope is zero, that is:

$1-5siny=0\Rightarrow siny=\frac{1}{5}\Rightarrow y=arcsin(\frac{1}{5})\\y=1.732,1.525, 3.063 \text{ etc.}$

5 0

2 years ago