Question

note: triangle may not be drawn to scale. suppose a = 2 and b = 10. find an exact value or give at least two decimal places: sin(a) = blank cos(a) = blank tan(a) = blank sec(a) = blank csc(a) = blank cot(a) = blank question help: video

Explanation:

Step1: Find hypotenuse c

$c=\sqrt{a^{2}+b^{2}}=\sqrt{2^{2}+10^{2}}=\sqrt{4 + 100}=\sqrt{104}=2\sqrt{26}$

Step2: Calculate sin(A)

$\sin(A)=\frac{a}{c}=\frac{2}{2\sqrt{26}}=\frac{1}{\sqrt{26}}\approx0.19$

Step3: Calculate cos(A)

$\cos(A)=\frac{b}{c}=\frac{10}{2\sqrt{26}}=\frac{5}{\sqrt{26}}\approx0.98$

Step4: Calculate tan(A)

$\tan(A)=\frac{a}{b}=\frac{2}{10}=0.2$

Step5: Calculate sec(A)

$\sec(A)=\frac{c}{b}=\frac{2\sqrt{26}}{10}=\frac{\sqrt{26}}{5}\approx1.02$

Step6: Calculate csc(A)

$\csc(A)=\frac{c}{a}=\frac{2\sqrt{26}}{2}=\sqrt{26}\approx5.10$

Step7: Calculate cot(A)

$\cot(A)=\frac{b}{a}=\frac{10}{2}=5$

Answer:

$\sin(A)\approx0.19$
$\cos(A)\approx0.98$
$\tan(A)=0.2$
$\sec(A)\approx1.02$
$\csc(A)\approx5.10$
$\cot(A)=5$