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Use the tables to find the tangents of the following angles: 13°, 64°, 35°, 56° and find the angles whose tangents are 0.9556.

Mathematics

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Answers

3 parts
a

43.69∘43.69^\circ

b

66.80∘66.80^\circ

c

32.60∘32.60^\circ

Step-by-step solution

10 steps

Let's solve these trigonometry problems. Since the specific tables are not provided, I will use a calculator to find the tangent values and angles.

: Use the tables to find the tangents of the following.

  1. Find tan⁡(13∘)\tan(13^\circ)

    Step 1: Use a calculator to find the tangent of 13∘13^\circ.

    tan⁡(13∘)≈0.230868\tan(13^\circ) \approx 0.230868

    Step 2: Round to four decimal places.

    tan⁡(13∘)≈0.2309\tan(13^\circ) \approx \boxed{0.2309}

  2. Find tan⁡(64∘)\tan(64^\circ)

    Step 1: Use a calculator to find the tangent of 64∘64^\circ.

    tan⁡(64∘)≈2.050304\tan(64^\circ) \approx 2.050304

    Step 2: Round to four decimal places.

    tan⁡(64∘)≈2.0503\tan(64^\circ) \approx \boxed{2.0503}

  3. Find tan⁡(35∘)\tan(35^\circ)

    Step 1: Use a calculator to find the tangent of 35∘35^\circ.

    tan⁡(35∘)≈0.700207\tan(35^\circ) \approx 0.700207

    Step 2: Round to four decimal places.

    tan⁡(35∘)≈0.7002\tan(35^\circ) \approx \boxed{0.7002}

  4. Find tan⁡(56∘)\tan(56^\circ)

    Step 1: Use a calculator to find the tangent of 56∘56^\circ.

    tan⁡(56∘)≈1.482560\tan(56^\circ) \approx 1.482560

    Step 2: Round to four decimal places.

    tan⁡(56∘)≈1.4826\tan(56^\circ) \approx \boxed{1.4826}

Example 7: Use tables to find the angles whose tangents are:

Part a· 3 steps

**tan⁡θ=0.9556\tan \theta = 0.9556

  1. Use the inverse tangent function (arctan⁡\arctan or tan⁡−1\tan^{-1}) to find the angle θ\theta.

    $$
\theta = \arctan(0.9556)
$$

  2. Calculate the value.

    $$
\theta \approx 43.690^\circ
$$

  3. Round to two decimal places.

    $$
\theta \approx \boxed{43.69^\circ}
$$

Part b

66.80∘66.80^\circ

**tan⁡θ=73\tan \theta = \frac{7}{3}

  1. Convert the fraction to a decimal.

    $$
\frac{7}{3} \approx 2.333333
$$

  2. Use the inverse tangent function to find the angle θ\theta.

    $$
\theta = \arctan\left(\frac{7}{3}\right) \approx \arctan(2.333333)
$$

  3. Calculate the value.

    $$
\theta \approx 66.801^\circ
$$

  4. Round to two decimal places.

    $$
\theta \approx \boxed{66.80^\circ}
$$

Part c

32.60∘32.60^\circ

**tan⁡θ=0.6398\tan \theta = 0.6398

  1. Use the inverse tangent function to find the angle θ\theta.

    $$
\theta = \arctan(0.6398)
$$

  2. Calculate the value.

    $$
\theta \approx 32.599^\circ
$$

  3. Round to two decimal places.

    $$
\theta \approx \boxed{32.60^\circ}
$$
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