43. Compute the value of \( \cot 60 \) A. \( \frac{1}{\sqrt{2}} \) B. \( \frac{1}{\sqrt{3}} \) C. \( \sqrt{3} \) D. 1 44. If \( \tan \theta=1.4276 \), then \( \sec \theta \) is equal to: A. 0.8190 B. 0.5737 C. 0.7005 D. 1.743 45. The value of \( \cos \left(\frac{-3 \pi}{4}\right) \), correct to 3 decimal places, is A. 0.999 B. 0.707 C. -0.999 D. -0.707

Let's solve each problem step by step. --- ### **43. Compute the value of \( \cot 60^\circ \)** **Options:** - **A.** \( \frac{1}{\sqrt{2}} \) - **B.** \( \frac{1}{\sqrt{3}} \) - **C.** \( \sqrt{3} \) - **D.** 1 **Solution:** The cotangent function is the reciprocal of the tangent function: \[ \cot 60^\circ = \frac{1}{\tan 60^\circ} \] We know that: \[ \tan 60^\circ = \sqrt{3} \] Therefore: \[ \cot 60^\circ = \frac{1}{\sqrt{3}} \] **Answer:** **B. \( \frac{1}{\sqrt{3}} \)** --- ### **44. If \( \tan \theta=1.4276 \), then \( \sec \theta \) is equal to:** **Options:** - **A.** 0.8190 - **B.** 0.5737 - **C.** 0.7005 - **D.** 1.743 **Solution:** Using the trigonometric identity: \[ 1 + \tan^2 \theta = \sec^2 \theta \] Plugging in the given value: \[ 1 + (1.4276)^2 = \sec^2 \theta \\ 1 + 2.037 = \sec^2 \theta \\ 3.037 = \sec^2 \theta \\ \sec \theta = \sqrt{3.037} \approx 1.743 \] **Answer:** **D. 1.743** --- ### **45. The value of \( \cos \left(\frac{-3 \pi}{4}\right) \), correct to 3 decimal places, is:** **Options:** - **A.** 0.999 - **B.** 0.707 - **C.** -0.999 - **D.** -0.707 **Solution:** First, recognize that cosine is an even function: \[ \cos(-\theta) = \cos(\theta) \] Thus: \[ \cos\left(\frac{-3\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) \] \[ \frac{3\pi}{4} \text{ radians } = 135^\circ \] \[ \cos(135^\circ) = -\frac{\sqrt{2}}{2} \approx -0.7071 \] Rounded to three decimal places: \[ \cos\left(\frac{-3\pi}{4}\right) \approx -0.707 \] **Answer:** **D. -0.707** ---