Answer:
Part 1) [tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]
cosine theta equals plus or minus square root of seven over 4
Part 2) [tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]
tangent theta equals plus or minus three over square root of seven
or
[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]
tangent theta equals plus or minus three times square root of seven over seven
Step-by-step explanation:
we have that
The sine of angle theta is equal to
[tex]sin(\theta)=\frac{3}{4}[/tex]
Is positive
therefore
The angle theta lie on the I Quadrant or in the II Quadrant
Part 1) Find the value of the cosine of angle theta
Remember that
[tex]sin^{2} (\theta)+cos^{2} (\theta)=1[/tex]
we have
[tex]sin(\theta)=\frac{3}{4}[/tex]
substitute and solve for cosine of angle theta
[tex](\frac{3}{4})^{2}+cos^{2} (\theta)=1[/tex]
[tex]cos^{2} (\theta)=1-(\frac{3}{4})^{2}[/tex]
[tex]cos^{2} (\theta)=1-\frac{9}{16}[/tex]
[tex]cos^{2} (\theta)=\frac{7}{16}[/tex]
[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]
cosine theta equals plus or minus square root of seven over 4
Part 2) Find the value of tangent of angle theta
we know that
[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]
we have
[tex]sin(\theta)=\frac{3}{4}[/tex]
[tex]cos(\theta)=(+/-)\frac{\sqrt{7}}{4}[/tex]
substitute
[tex]tan(\theta)=\frac{\frac{3}{4}}{(+/-)\frac{\sqrt{7}}{4}}[/tex]
[tex]tan(\theta)=(+/-)\frac{3}{\sqrt{7}}[/tex]
tangent theta equals plus or minus three over square root of seven
Simplify
[tex]tan(\theta)=(+/-)3\frac{\sqrt{7}}{7} [/tex]
tangent theta equals plus or minus three times square root of seven over seven
