Definition
Adjacent angles are two angles in a plane that have a common vertex and a common side but no common interior points.
Examples
Angles 1 and 2 are adjacent angles because they share a common side.
adjacent angles examples
5
If tan θ = —— , calculate the value of cos θ:
4
Recall the definition of the tangent function:
sin θ
tan θ = ————
cos θ
5 sin θ
—— = ————
4 cos θ
Cross multiply:
5 · cos θ = 4 · sin θ
Square both sides:
(5 · cos θ)² = (4 · sin θ)²
5² · cos² θ = 4² · sin² θ
25 · cos² θ = 16 · sin² θ
But sin² θ = 1 – cos² θ. Substitute that for sin² θ into the equation above, then you get
25 · cos² θ = 16 · (1 – cos² θ)
25 · cos² θ = 16 – 16 · cos² θ
Isolate cos² θ:
25 · cos² θ + 16 · cos² θ = 16
(25 + 16) · cos² θ = 16
41 · cos² θ = 16
16
cos² θ = ———
41
4²
cos² θ = ————
(√41)²
Take square root of both sides:
4
cos θ = ± ———
√41
4 4
cos θ = – ——— or cos θ = ——— ✔
√41 √41
The sign of cos θ depends on which quadrant θ lies. Since you first have a positive value for tan θ, then that means θ lies either in the 1st or the 3rd quadrant.
• If θ is a 1st quadrant angle, then
cos θ > 0
4
cos θ = ——— ✔
√41
• If θ is a 3rd quadrant angle, then
cos θ < 0
4
cos θ = – ——— ✔
√41
I hope this helps. =)
Answer:
1
Step-by-step explanation:
Rise/run
<em>Answer:</em>
<em>Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over </em>
<em>10 1
</em>
<em> (10
). Next, add the whole number to the left of the decimal.
</em>
<em>1 2
/10
</em>
<em>Reduce the fractional part of the mixed number.
</em>
<em>1 1
/5
</em>
<em>Reduce the fraction.
</em>
<em>6/
5
</em>
<em />
<em>Step-by-step explanation:</em>
<em />
The answer is Angle ACB
The angle is form from both line A and C
