1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
omeli [17]
3 years ago
7

What is the half-angle of tangent 22.5 (degrees)?

Mathematics
2 answers:
Sergio039 [100]3 years ago
6 0

Find tan (22.5)

Answer: #-1 + sqrt2#

Explanation:

Call tan (22.5) = tan t --> tan 2t = tan 45 = 1

Use trig identity: # tan 2t = (2tan t)/(1 - tan^2 t)# (1)

#tan 2t = 1 = (2tan t)/(1 - tan^2 t)# -->
--> #tan^2 t + 2(tan t) - 1 = 0#
Solve this quadratic equation for tan t.

#D = d^2 = b^2 - 4ac = 4 + 4 = 8# --> #d = +- 2sqrt2#
There are 2 real roots:
tan t = -b/2a +- d/2a = -2/1 + 2sqrt2/2 = - 1 +- sqrt2
Answer:
#tan t = tan (22.5) = - 1 +- sqrt2#
Since tan 22.5 is positive, then take the positive answer:
tan (22.5) = - 1 + sqrt2


irina [24]3 years ago
6 0
Since <span>22.522.5</span> is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.<span>22.522.5</span> is not an exact angleFirst, rewrite the angle as the product of <span><span>12</span><span>12</span></span> and an angle where the values of the six trigonometric functions are known. In this case, <span>22.522.5</span> can be rewritten as <span><span><span>(<span>12</span>)</span>⋅45</span><span><span>12</span>⋅45</span></span>.<span><span>tan<span>(<span><span>(<span>12</span>)</span>⋅45</span>)</span></span><span>tan<span><span>12</span>⋅45</span></span></span>Use the half-angle identity for tangent to simplify the expression. The formula states that <span><span><span><span><span>ta</span>n</span><span>(<span>θ2</span>)</span></span>=<span><span>sin<span>(θ)</span></span><span>1+<span>cos<span>(θ)</span></span></span></span></span><span><span><span><span>ta</span>n</span><span>θ2</span></span>=<span><span>sinθ</span><span>1+<span>cosθ</span></span></span></span></span>.<span><span><span>sin<span>(45)</span></span><span>1+<span>cos<span>(45)</span></span></span></span><span><span>sin45</span><span>1+<span>cos45</span></span></span></span>Simplify the result.
<span><span>√2</span><span>−<span>1</span></span></span>
You might be interested in
97 people are surveyed and 32 of them agree with closing campus for lunch. Is it discrete or continuous
Anton [14]

Discrete

It is a specific value

4 0
3 years ago
WORTH 60 POINTS! PLZ HELP! BRAINLIEST OPPORTUNITY!
makkiz [27]

Answer:

x = 10

Step-by-step explanation:

2) -3x + 17 = -x - 3

4) 20 = 2x

1) -3x + 12 + 5 = -x -3

5) 10 = x

3) 17 = 2x - 3

<u>-3(x - 4) + 5 = -x - 3</u>

<u>-3x + 12 + 5 = -x - 3</u>

<u>-3x + 17 = -x -3</u>

<em>+3x          +3x</em>

<u>17 = 2x - 3</u>

<em>+3        + 3</em>

<u>20 = 2x</u>

<u>10 = x</u>

<u />

I hope that this helps! :)

5 0
3 years ago
Is a megabyte bigger than a gigabyte.
san4es73 [151]

Answer:

NO!!! Megabytes AREN'T bigger than Gigabytes!

Step-by-step explanation:

Here's the table!

1 Kilobyte = 1,024 Bytes

1 Megabyte = 1,024 Kilobytes

1 Gigabyte = 1,024 Megabytes

1 Terabyte = 1,024 Gigabytes

<h2>From this we can see that Megabyte <em>ISN'T</em> bigger than Gigabyte</h2>
6 0
2 years ago
The sampling distribution of the ratio of two independent sample variances selected randomly from normal populations with equal
Likurg_2 [28]

Answer:  F distribution. chi-square distribution. t distribution. normal distribution.

Step-by-step explanation:

5 0
2 years ago
If you received a 5% raise and your final paycheck was 100(which includes your 5% raise), how much was your original paycheck?
Schach [20]

so you were earning say "x", so "x" is the 100% of  your paycheck.

but you're da bomb and so you got a raise of 5%, so the new amount of your paycheck is 100% + 5%, so is 105% really, and we happen to know that is $100.


\bf \begin{array}{ccll} \$&\%\\ \cline{1-2} 100&105\\ x&100 \end{array}\implies \cfrac{100}{x}=\cfrac{105}{100}\implies 10000=105x \\\\\\ \cfrac{10000}{105}=x\implies 95.238\approx x

8 0
3 years ago
Other questions:
  • Plz help w this (it’s not that hard)25+ points
    8·1 answer
  • Which form of cell division plays a key role in sexual reproduction? A. budding B. meiosis C. mitosis D. conjugation
    12·2 answers
  • Shelly and Terrence completed a different number of tasks in a game. Shelly earned 90 points on each task. Terrence's total poin
    9·2 answers
  • In the month of March, the temperature at the South Pole varies over the day in a periodic way that can be modeled approximately
    13·1 answer
  • Which answer gives statements that should be used to prove angles 4 and 6 are congruent?
    6·1 answer
  • Three players scored a total of 70 points during a basketball game. One player scored twice as many as one teammate and ten poin
    11·1 answer
  • 10 x 4 ones = ones =
    6·2 answers
  • Kelsey babysat for 4 hours and earned $25.00. How much did Kelsey earn per hour?
    11·2 answers
  • A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many k
    12·2 answers
  • I NEED HELP!!!! I am currently reviewing for my last test, and i am struggling with this problem. I KNOW WHAT THE ANSWER IS BUT
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!