Chapter 5 Geometry

Section 5.6 Trigonometric Functions: Sine, et cetera

5.6.4 Exercises

Exercise 5.6.9
What is the degree measure of the angle $\phi$ between the $x$-axis and the connecting line from the origin in the Cartesian coordinate system to the point ${P}_{\phi }=\left(-0.643;-0.766\right)$ on the unit circle? Use a calculator, but do not trust it blindly!
Result: $\phi$$=$
${}^{\circ }$

Exercise 5.6.10
1. Let a right triangle with the right angle at the vertex $C$ and the sides $b=2.53 \mathrm{cm}$ and $c=3.88 \mathrm{cm}$ be given. Calculate the values of $\mathrm{sin}\left(\alpha \right)$, $\mathrm{sin}\left(\beta \right)$, and $a$.
Results:
• $\mathrm{sin}\left(\alpha \right)$$=$
• $\mathrm{sin}\left(\beta \right)$$=$
• $a$$=$
$\mathrm{cm}$

2. Calculate the area $F$ of a triangle with the sides $a=4 \mathrm{m}$, $c=60 \mathrm{cm}$, and the angle $\beta =\measuredangle \left(a,c\right)=\frac{11\pi }{36}$.
Result: $F$$=$
$\mathrm{m}{}^{2}$
Please, enter your result rounded to three decimal digits or as an expression. Enter the sine of an angle as sin(x) and the number $\pi$ as pi.