Question

Trigonometry

Answer 1

Answer:

3√15/4

Step-by-step explanation:

sin x = 2/8

• from the trigonometric rule sin²x+cos²x = 1
• cos²x = 1-sin²x

sinx = 2/8

sin²x = (2/8)² = 2²/8² = 4/64

1- sin²x = 1-4/64 = 64 -4/64 = 60/64 = 15/16

• cos²x = 15/16

cos x = √(15/16) = √15 /4

• cos 3x

3 x cos x = 3 x √15/4 = 3√15/4

Answer 2

Answer:

$cos3x=\frac{3\sqrt{15}}{16}$

Step-by-step explanation:

Notes that:

$sinx=\frac{2}{8}=\frac{1}{4}$.

We use sinx to find cosx:

$cos^2x=1-sin^2x=1-(\frac{1}{4})^2=\frac{15}{16}$, then

$cosx=\frac{\sqrt{15}}{4}$.

Now we use formule for double angle of sin and cos, to find cos2x and sin2x:

$sin2x=2sinxcosx=2*\frac{1}{4}*\frac{\sqrt{15}}{4}=\frac{\sqrt{15}}{8}$

$cos2x=cos^2x-sin^2x=\frac{15}{16}-\frac{1}{16}=\frac{14}{16}=\frac{7}{8}$

Now, we can find cos3x:

$cos3x=cos(2x+x)=cos2x*cosx-sin2x*sinx=$

$\frac{7}{8}*\frac{\sqrt{15}}{4}-\frac{\sqrt{15}}{8}*\frac{1}{4}$

$cos3x=\frac{7\sqrt{15}{32}-\frac{\sqrt{15}}{32}=$

$\frac{6\sqrt{15}}{32}=\frac{3\sqrt{15}}{16}$