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Use tables to determine the angles whose tangents are a) 0.1638 b) 2.9544 c) 5.9758 d) 10.019

Mathematics

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4 parts
a

9.30∘\text{9.30}^\circ

b

71.30∘\text{71.30}^\circ

c

80.49∘\text{80.49}^\circ

d

84.29∘\text{84.29}^\circ

Step-by-step solution

8 steps

Ili kupata pembe ambazo tangenti zake zimetolewa, tutatumia kazi ya inverse tangent (tan⁡−1\tan^{-1}) au kutafuta thamani hizi kwenye jedwali la tangenti.

Part a· 2 steps

  1. Tafuta pembe θ\theta ambayo tan⁡(θ)=0.1638\tan(\theta) = 0.1638.

    θ=tan⁡−1(0.1638)\theta = \tan^{-1}(0.1638)

  2. Kokotoa thamani.

    θ≈9.30∘\theta \approx 9.30^\circ

    Pembe ni 9.30∘\boxed{\text{9.30}^\circ}.

Part b

71.30∘\text{71.30}^\circ

  1. Tafuta pembe θ\theta ambayo tan⁡(θ)=2.9544\tan(\theta) = 2.9544.

    θ=tan⁡−1(2.9544)\theta = \tan^{-1}(2.9544)

  2. Kokotoa thamani.

    θ≈71.30∘\theta \approx 71.30^\circ

    Pembe ni 71.30∘\boxed{\text{71.30}^\circ}.

Part c

80.49∘\text{80.49}^\circ

  1. Tafuta pembe θ\theta ambayo tan⁡(θ)=5.9758\tan(\theta) = 5.9758.

    θ=tan⁡−1(5.9758)\theta = \tan^{-1}(5.9758)

  2. Kokotoa thamani.

    θ≈80.49∘\theta \approx 80.49^\circ

    Pembe ni 80.49∘\boxed{\text{80.49}^\circ}.

Part d

84.29∘\text{84.29}^\circ

  1. Tafuta pembe θ\theta ambayo tan⁡(θ)=10.019\tan(\theta) = 10.019.

    θ=tan⁡−1(10.019)\theta = \tan^{-1}(10.019)

  2. Kokotoa thamani.

    θ≈84.29∘\theta \approx 84.29^\circ

    Pembe ni 84.29∘\boxed{\text{84.29}^\circ}.

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